Find a vector vec r of magnitude 3sqrt(2) units which makes an angle of pi/4 and pi/2 with y an...

Find a vector vec r of magnitude 3sqrt(3) units which makes an angle of (pi)/(4) and (pi)/(2) with y and z- axis respectively.

Find a vector vec a of magnitude 5sqrt(2) making an angle of (pi)/(4) with x -axis,(pi)/(2) with y -axis and an acute angle theta with z -axis.

Find a vector vec a of magnitude 5sqrt(2) making an angle (pi)/(4) with x -axis,(pi)/(2) with y -axis and an acute angle theta with z -axis

If a vector vec r of magnitude 3sqrt(6) is directed along the bisector of the angle between the vectors vec a=7vec i-4vec j-4vec k and vec b=-2vec i-vec j+2vec k, then vec r is equal to

vec(a) "and" vec(b) are two given mutually perpendicular vectors such that |vec(a)|=4 "and" |vec(b)| =3. vec(c ) is a unit vector making an angle of (pi)/(4) and (pi)/(3) with vec(a) "and" vec(b) respectively. If (x,y) represents the number of possible vector vec(c) and the volume of tetrahedron formed by vectors vec(a), vec(b),vec(c) as adjacent sides respectively, then (x,y) is

Find the vector sum of N coplanar forces, each of the magnitude F ,when each force makes an angle of 2pi//N with that preceding it.

Let vec n be a vector of magnitude 2sqrt(3) such that it makes equal acute angle with the coordinate axes.Find the vector and cartesian forms of the equation of plane passing from (1,-1,2) and normal to vec n.

Let vec n be a vector of magnitude 2sqrt(3) such that it makes equal acute angles with the coordinate axes.Find the vector and Cartesian forms of the equation of a plane passing through (1,-1,2) and normal to vec n.