If the vector is collinear with the vector (2√2, -1,4) 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
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 non-collinear 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 non-coplaner vectors and λ is a real number, then the vectors
are non-coplaner 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 non-zero 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
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