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.

The angle at which the normal vector to the plane 4x+8y+z=5 inclined to the Z-axis is

Find the angles at which the normal vector to the plane 4x+8y+z=5 is inclined to the coordinate axes.

If vec a and vec b are unit vectors find the angle between vec a+vec b and vec a-vec b

Suppose that vec p, vec q and vec r are three non-coplanar vectors in R^3. Let the components of a vector vec s along vec p, vec q and vec r be 4, 3 and 5, respectively. If the components of this vector vec s along (-vec p+vec q +vec r), (vec p-vec q+vec r) and (-vec p-vec q+vec r) are x, y and z, respectively, then the value of 2vec x+vec y+vec z is

A vector vec OP is inclined to OX at 45^(@) and OY at 60^(@). Find the angle at which vec OP is inclined to OZ

Find the direction cosines of a vector which is equally inclined to the x-axis, y-axis and z-axis.

If a vector vec A makes angles 45^(@) and 60^(@) with x and y axis respectively, then the angle made by it with z- axis is x times10^(@) find x

Find the angle between two vectors vec a and and with magnitudes 1and 2respectively and with magnitudes 1and 2respectively and when quad vec a*vec b=1

The angle subtended by vector vec(i)+vec(j) with x-axis is :-

If vec(i) and vec(j) are unit vectors along x-axis and y-axis respectively, the magnitude of vector vec(i)+vec(j) will be :-