एक बिंदु `(2, 5, -3) = 4` की समतल `overline(r) (6hat(i) - 3hat(j) + 2hat(k)) = 4` से दूरी ज्ञात कीजिये।

If overline(a)*hat(i)=4, then (overline(a)timeshat(j))*(2hat(j)-3hat(k))=

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))

Find the distance of a point (2,5,-3) from the plane vec r*(6hat i-3hat j+2hat k)=4

A body is displaced from vec r_(A) =(2hat i + 4hatj -6hat k) to vecr_(B) = (6hat i -4hat j +3 hat k) under a constant force vec F = (2 hat i + 3 hat j - hat k) . Find the work done.

Find out whether the following pairs of lines are parallel, non parallel, & intersecting, or non-parallel & non-intersecting. vec(r_(1)) = hat(i) - hat(j) + 3hat(k) + lambda(hat(i) - hat(j)+hat(k)) vec(r_(2)) = hat(i) - hat(j) + 3hat(k) + lambda(hat(i) - hat(j) + hat(k)) vec(r_(2)) = 2hat(i) + 4hat(j) + 6hat(k) + mu (2hat(i) + hat(j) + 3hat(k))

Following forces start acting on a particle at rest at the origin of the co-ordinate system overset(rarr)F_(1)=-4 hat I -5 hat j +5hat k , overset(rarr)F_(2)=5hat I +8 hat j +6hat k , overset(rarr)F_(3)=-3hat I + 4 hat j - 7 hat k and overset(rarr)F_(4)=2hat i - 3 hat j - 2 hat k then the particle will move

vec(r ) =(hat(i) +2hat(j) +3hat(k)) + lambda(hat(i) -3hat(j) +2hat(k)) vec(r ) =(4hat(i) +5hat(j) +6hat(k)) + mu (2hat(i) + hat(j) +2hat(k)) Find the the shortest between the lines

Given vectors overline(a)=3hat(i)-6hat(j)-hat(k), overline(b)=hat(i)+4hat(j)-3hat(k), overline(c)=3hat(i)-4hat(j)-12hat(k) , then the projection of overline(a)timesoverline(b) on vector overline(c) is