The distance of the plane `overset(to) (r ) ((2)/(7) hat(i) + (3)/(7) hat(j) - (6)/(7) hat(k) )= 1` from the origins is.

A vector parallel to the line of intersection of the planes overset(to)( r) (3 hat(i) - hat(j) + hat(k) )=5 and overset(to) (r ) (hat(i) +4 hat(j) - 2 hat(k) )=3 is

The angle between the lines overset(to)( r)=(4 hat(i) - hat(j) )+ lambda(2 hat(i) + hat(j) - 3hat(k) ) and overset(to) (r )=( hat(i) -hat(j) + 2 hat(k) ) + mu (hat(i) - 3 hat(j) - 2 hat(k) ) is

Consider the plane through (2, 3, -1) and at right angles to the vector 3hat(i)-4hat(j)+7hat(k) from the origin is

Find the volume of the parallelepiped whose edges are represented by the vectors overset(to) (a) = 2 hat(i) - 3 hat(j) -4 hat(k), overset(to)( b) = hat(i) + 2 hat(j) - hat(k) , overset(to)( c) =3 hat(i) - hat(j) - 2 hat(k) .

If the planes overset(to)( r) (2 hat(i) - lambda (j) + 3 hat(k) ) = 0 and overset(to)( r) ( lambda (i) + 5 hat(j) - hat(k) )=5 are perpendicular to each other, then the value of lambda is

Find the distance of the point (3, 3, 3) from the plane vec r.(5 hat i+2 hat j-7 hat k)+9=0

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Calculate the magnitude of the vector, overset(rarr)r =(3 hat i+4 hat j + 7hat k) metre.

The torque of force F = -3 hat(i)+hat(j) + 5 hat(k) acting on a point r = 7 hat(i) + 3 hat(j) + hat(k) about origin will be

Find the equation of the plane passing through the intersection of the planes vec r .(2 hat i+ hat j+3 hat k)=7, vec r.(2 hat i+5 hat j+3 hat k)=9 the point (2,1,3)dot