If the vector is collinear with the vector (2√2, 14) and = 10, then
The vertices of a triangle are A(1, 1, 2), B(4, 3, 1) and C(2, 3, 5). A vector representing the internal bisector of the angle A is
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Angle between diagonals of a parallelogram whose side are represented by
Vector make an angle θ = 2π/3. if , then is equal to
Unit vector perpendicular to the plane of the triangle ABC with position vectors of the vertices
A, B, C is
If are two noncollinear vectors such that , then is equal to
Vector of length 3 unit which is perpendicular to and lies in the plane of and
If ^{a ,b,c} are linearly independent vectors, then which one of the following set of vectors is linearly dependent ?
Let be vectors of length 3,4,5 respectively. Let be perpendicular to , and . then
Given the vertices A (2, 3, 1), B(4, 1, –2), C(6, 3, 7) & D(–5, –4, 8) of a tetrahedron. The length of the altitude drawn from the vertex D is
for a non zero vector If the equations hold simultaneously, then
The volume of the parallelopiped constructed on the diagonals of the faces of the given rectangular parallelopiped is m times the volume of the given parallelopiped. Then m is equal to
If u and v are unit vectors and θ is the acute angle between them, then 2u × 3v is a unit vector for
The value of a, for which the points A,B,C with position vectors and respectively are the vertices of a right angled triangle with C = π/2 are
A particle is acted upon by constant forces which displace ot from a point to the point . The workdone in standard units by the force is given by
If are noncoplaner vectors and λ is a real number, then the vectors are noncoplaner for
Let be non zero vectors such that , If θ is the acute angle between the vectors , then sin θ equals is
The vectors are the sides of a triangle ABC. The length of the median through A is
Let and be three nonzero vectors such that is a unit vector perpendicular to both . if the angle between is π/6, then is equal to
A point taken on each median of a triangle divides the median in the ratio 1 : 3, reckoning from the vertex.
Then the ratio of the area of the triangle with vertices at these points to that of the original triangle is
204 videos288 docs139 tests

204 videos288 docs139 tests
