दो रेखाओ जिनके सदिश समीकरण `vec(r ) = (3-t) hat(i) + ( 4- 2t ) hat(j) + (t-2) hat(k) ` तथा ` vec(r) = (1+s) hat(i) + (3s - 7 ) hat(j) + (2s - 2) hat(k)` है , के बीच की न्यूनतम दूरी ज्ञात कीजिए।

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

Find the Cartesian form of the equation of the plane vec(r)=(s-2t)hat(i)+(3-t)hat(j)(2s+t)hat(k)

The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

Let vec( a) = 2 hat(i) - 3 hat(j) + 4 hat(k) and vec( b) = 7 hat(i) + hat(j) - 6 hat(k) . If vec( r ) xx vec( a) = vec( r ) xx vec( b) , vec( r ) . ( hat(i) +2 hat(j) + hat(k)) = -3 , then vec ( r ). ( 2 hat(i)- 3hat(j) + hat(k)) is equal to :