The scalar equals :
For nonzero vectors holds if and only if
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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
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209 videos443 docs143 tests
