A straight line which makes an angle of 60^o with each of y and z-axes, this line makes with x-axes at an angle

What are the DR's of vector parallel to ( 2 , -1 , 1) and ( 3, 4 , -1 ) ?

The ratio in which yz-plane divides the line segment joining (-3,4,-2) and (2,1,3) is

The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1,-1,2) and (2,1,-1) are

A point on XOZ-plane divides the join of (5,-3,-2) and (1,2,-2) at

Let A(1,-1,2) and B (2,3,-1) be two points. If a point P divides AB internally in the ratio 2 : 3, then the position vector of P is

The vectors of magnitude a , 2a , 3a meet at a point and their directions are along the diagonals of three adjacent faces of a cube. Then, the magnitude of their resultant is

A line AB in three-dimensional space makes angles 45^o and 120^o with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

Cosine of the angle between two diagonals of cube is equal to 

The projection of the line segment joining the points. (-1,0,3) and (2,5,1) 0n the line whose direction ratios are 6,2,3 is