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.

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

A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find the angle at which vec O P is inclined to O Zdot

A vector vec O P is inclined to O X at 45^0 and O Y at 60^0 . Find the angle at which vec O P is inclined to O Zdot

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

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

A = vec(i) + vec(j) . What is the angle between the vector and x-axis ?

Find the vector equation of the plane with intercepts 3,-4 and 2 on x ,y and z-axis respectively.

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

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

Find the angle between two vectors vec a and vec b with magnitudes sqrt(3) and 2 respectively having vec a. vec b=sqrt(6)