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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 1

The scalar equals :

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 2

For non-zero vectors holds if and only if

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 3

The volume of the parallelopiped whose sides are given by

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 4

The points with position vectors 60i + 3j, 40 i – 8 j, ai – 52 j are collinear if

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 5

Let be three non - coplanar vectors and are vectors defined by the relations then the value of the expression is equal to

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 6

Let a, b, c be distinct non-negative numbers. If the vectors lie in a plane, then c is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 7

Let be the position vectors of P and Qr espectively, with respect to O and The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If OR and OS are perpendicular then

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 8

Let α, β, γ be distinct real numbers. The points with position vectors

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 9

Let is a unit vector such that equals

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 10

If are non coplanar unit vectors such that then the angle between is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 11

Let be vectors such that If and

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 12

If are three non coplanar vectors, then equals

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 13

Let a = 2i + j – 2k and b = i + j. If c is a vector such that a. c = | c |, | c - a | = 2√2 and the angle between (a × b) and c is 30°, then | (a × b) × c| =

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 14

Let a =2i + j + k, b = i +2j –k and a unit vector c be coplanar. If c is perpendicular to a, then c =

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 15

If the vectors form the sides BC, CA and ABrespectively of a triangle ABC, then

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 16

Let the vectors be such that Let P_{1} and P_{2} be planes determined by the pairs of vectors respectively. Thenthe angle between P_{1} and P_{2} is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 17

If are unit coplanar vectors, then the scalar triple product

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 18

and depends on

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 19

If are unit vectors, then does NOT exceed

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 20

are two unit vectors such that and are perpendicular to each other then the angle between

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 21

Let is a unit vector,, then the maximum value of the scalar triple product

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 22

The value of k such that lies in the plane 2x – 4y + z = 7, is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 23

The value of ‘a’ so that the volume of parallelopiped formed by becomes minimum is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 24

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 25

If the lines

intersect, then the value of k is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 26

The unit vector which is orthogonal to the vector an d is coplanar with the vectors and

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 27

A variable plane at a distance of the one unit from the origin cuts the coordinates axes at A, B and C. If the centroid D (x, y, z) of triangle ABC satisfies the relation , then the value k is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 28

If are three non-zero, non-coplanar vectors and

then the set of orthogonal vectors is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 29

A plane which is perpendicular to two planes 2x – 2y + z = 0 and x – y + 2z = 4, passes through (1, –2, 1). The distance of the plane from the point (1, 2, 2) is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 30

L et A vector in the plane of whose projection on

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 31

The number of distinct real values of λ, for which the vectors are coplanar, is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 32

Let be unit vectors such that Which one of the following is correct ?

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 33

The edges of a parallelopiped are of unit length and are parallel to non-coplan ar unit vectors such that Then, the volume of the parallelopiped is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 34

Let two non-collinear unit vectors form an acute angle. A point P moves so that at any time t the position vector (where O is the origin) is given by When P is farthest from origin O, let M be the length of and be the unit vector along

Then,

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 35

Let P (3, 2, 6) be a point in space and Q be a point on the line

Then the value of m for which the vector is parallel to the plane x – 4y + 3z = 1 is

Detailed Solution for JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 35

JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 36

are unit vectors such that

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 37

A line with positive direction cosines passes through the point P(2, –1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 38

Let P, Q, R and S be the points on the plane with position vectors respectively. The quadrilateral PQRS must be a

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 39

Equation of the plane containing the straight line and perpendicular to the plane containing the

straight lines

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 40

If the distance of the point P (1, –2, 1) from the plane x + 2y –2z = α, where α > 0, is 5, then the foot of the perpendicular from P to the plane is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 41

Two adjacent sides of a parallelogram ABCD are given by

The side AD is rotated by an acute angle a in the plane of the parallelogram so that AD becomes AD¢. If AD¢ makes a right angle with the side AB, then the cosine of the angle a is given by

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 42

Let be three vector s. A vector the plane of whose projection on , is given by

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 43

The point P is the intersection of the straight line joining the points Q(2, 3, 5) and R(1, –1, 4) with the plane 5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR, then the length of the line segment PS is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 44

The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x – y + z = 3 and at a distance from the point (3, 1 ,–1) is

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 45

If are vectors such that and then a possible value of

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JEE Advanced (Single Correct MCQs): Vector Algebra and Three Dimensional Geometry - Question 46

Let P be the image of the point (3,1,7) with r espect to the plane x – y + z = 3. Then the equation of the plane passing through P and containing the straight line

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