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.

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

A vector makes angle with X,Y and Z axes that are in the ratio 1:2:1 respectively. The angle made by the vector with Y-axis is

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

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

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

Suppose that vec(p), vec(q) and vec(r) are three non-coplanar vectors in R. 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 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