A vector `vec(r )` is inclined at equal angles to the three axes. If the magnitude of `vec(r )` is `2sqrt(3)` units, find `vec(r )` .

A vector vecv is inclined at equal angles to the positive directions of the three coordinate axes. If the magnitude of vecv is 6 units, find vecv .

If vec a, vec b and vec c are three non-coplanar unit vectors each inclined with other at an angle of 30^@, then the volume of tetrahedron whose edges are vec a,vec b, vec c is (in cubic units)

Find the angle between the vectors vec a and vec b with magnitudes 1 and 1 respectively and when vec a.vec b =1.

If vec a, vec b ,vec c are mutually perpendicular vectors of equal magnitudes, show that the vector vec a+ vec b + vec c is equally inclined to vec a, vec b and vec c .

Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p""a n d""/_B A D be an acute angle. If vec r is the vector that coincides with the altitude directed from the vertex B to the side AD, then vec r is given by (1) vec r=3 vec q-(3( vec pdot vec q))/(( vec pdot vec p)) vec p (2) vec r=- vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p (3) vec r= vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p (4) vec r=-3 vec q+(3( vec pdot vec q))/(( vec pdot vec p)) vec p

Let O be the origin and vec(OX) , vec(OY) , vec(OZ) be three unit vector in the directions of the sides vec(QR) , vec(RP),vec(PQ) respectively , of a triangle PQR. if the triangle PQR varies , then the manimum value of cos (P+Q) + cos(Q+R)+ cos (R+P) is

Find the component of vector vec PQ where: P(2,3), Q(5,-3). Also, find the magnitude of vec PQ .

Let vec a and vec b be two unit vectors and θ is the angle between them. Then vec a+vec b is a unit vector if

Find a vector of magnitude sqrt 51 which makes equal angles with the vectors vec a =1/3 (hat i-2 hat j+2 hat k) , vec b=1/5(-4 hat i -3 hat k) and 'vec c=hat j .