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

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

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

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

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

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

Let  is a unit vector such that   equals 

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

Let   be vectors such that   If  and

If  are three non coplanar vectors, then  equals

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| =

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

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

Let the vectors  be such that   Let P₁ and P₂ be  planes determined by the pairs of vectors   respectively. Thenthe angle between P₁ and P₂ is

If  are unit coplanar vectors, then the scalar triple product

 and  depends on

If   are unit vectors, then  does NOT exceed

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

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

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

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

If the lines

intersect, then the value of k is

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

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

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

then the set of orthogonal vectors is 

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  

L et  A vector in the plane of   whose projection on 

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

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

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

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,

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

 are unit vectors such that 

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

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

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

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

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

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

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

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

If   are vectors such that  and   then a possible  value of

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