If the projections of vector ` vec a` on `x` -, `y` - and `z` -axes are 2, 1 and 2 units ,respectively, find the angle at which vector ` vec a` is inclined to the `z` -axis.

A line is inclined to the x-axis at 45^@ and y-axis at 60^@ . Find the angle at which the line is inclined to z-axis.

Find the angle of vector vec a = 6 hat i + 2 hat j - 3 hat k with x -axis.

Suppose that vec p,vecqand vecr are three non- coplaner in R^(3) ,Let the components of a vector vecs along vecp , vec q and vecr be 4,3, and 5, respectively , if the components this vector vec s along (-vecp+vec q +vecr),(vecp-vecq+vecr) and (-vecp-vecq+vecr) are x, y and z , respectively , then the value of 2x+y+z is

A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction of the x and y axes respectively. Then the angle between vec(OP) and the z-axis is

A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction of x and y axes respectively. Then the angle between vec(OP) and z axis is

If vec a and vec b be two unit vectors such that vec a+ vec b is also a unit vector, then find the angle between vec a and vec b

Find the angle betweeen two vectors vec a and vec b with magnitudes 2 and 1 respectively and such that veca. vec b = sqrt3 .

A vector vec(OP) makes 60^(@) and 45^(@) with the positive direction of the x and y axes repectively. Then the angle between vec(OP) and the z axis is _______

vec u , vec va n d vec w are three non-coplanar unit vecrtors anf alpha,betaa n dgamma are the angles between vec ua n d vec v , vec va n d vec w ,a n d vec wa n d vec u , respectively, and vec x , vec ya n d vec z are unit vectors along the bisectors of the angles alpha,betaa n dgamma , respectively. Prove that [ vec xxx vec y vec yxx vec z vec zxx vec x]=1/(16)[ vec u vec v vec w]^2sec^2alpha/2sec^2beta/2sec^2gamma/2dot