बिंदु `(5, 2, -4)` से जाने वाली तथा सदिश `3hat(i) + 2hat(j) + 8hat(k)` के समान्तर रेखा का सदिश तथा कार्तीय समीकरणों को ज्ञात कीजिये

If 3hat(i)-2hat(j)+8hat(k) and 2hat(i)+xhat(j)+hat(k) are at right angles then x=

A force vec(F) = (4hat(i) - 3hat(j) - 5hat(k)) N moves a body for (3hat(i) + 6hat(j) + 3hat(k)) m to (ahat(i) - 8hat(j) + 5hat(k)) m. If the work done by the force is 8j, the value of .a. is

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

Find the shortest distance between the lines : vec(r) = (4hat(i) - hat(j)) + lambda(hat(i) + 2hat(j) - 3hat(k)) and vec(r) = (hat(i) - hat(j) + 2hat(k)) + mu (2hat(i) + 4hat(j) - 5hat(k))

If A,B,C and D are points whose position vectors are hat(i) + hat(j) + hat(k), 4hat(i) - hat(j) + 2hat(k), 5hat(i) + hat(j) , 7 hat(i) + 2hat(j) + 3hat(k) respectively, then the projection of AB on CD is

The , perpendicular vector on both of (3hat i +hat j + 2hat k) and (2hat i -2hat j +4hat k) is: