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The scalar equals :
For nonzero vectors holds if and only if
The volume of the parallelopiped whose sides are given by
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 nonnegative 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 P_{1} and P_{2} be planes determined by the pairs of vectors respectively. Thenthe angle between P_{1} and P_{2} 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 nonzero, noncoplanar 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 noncoplan ar unit vectors such that Then, the volume of the parallelopiped is
Let two noncollinear 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
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129 videos408 docs306 tests
