[" The point of intersection of the lines "],[vec r=7hat vec i+10hat j+13widehat k" and "],[+s(2hat vec i+3hat j+4widehat k)],[vec r=3hat i+5hat j+7widehat k+t(hat i+2hat j+3widehat k)" is "]

The point of intersection of the lines vec(r) = 7hat(i) + 10 hat(j)+ 13 hat(k) , vec(s) = (2hat(i) + 3hat(j)+4hat(k)) and vec(r) = 3hat(i) + 5hat(j) + 7hat(k) + t(hat(i) + 2hat(j) + 3hat(k)) is

The point of intersection of the line vec(r)=7hat(i)+10hat(j)+13hat(k)+s(2hat(i)+3hat(j)+4hat(k)) and vec(r)=3hat(i)+5hat(j)+7hat(k)+t(hat(i)+2hat(j)+3hat(k)) is :

A point on the line vec r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

A vector parallel to the line of intersection of the planes vec r=dot(3 hat i- hat j+ hat k)=1\ a n d\ vec rdot(( hat i+4 hat j-2 hat k)=2 is a. -2 hat i+7 hat j+13 hat k b. 2 hat i+7 hat j-13 hat k c. -2i-7j+13 k d. 2i+7j+13 k

A vector parallel to the line of intersection of the planes vec r=dot(3 hat i- hat j+ hat k)=1\ a n d\ vec rdot(( hat i+4 hat j-2 hat k)=2 is a. -2 hat i+7 hat j+13 hat k b. 2 hat i+7 hat j-13 hat k c. -2i-7j+13 k d. 2i+7j+13 k

The lines vec r=(hat i+hat j+hat k)alpha+3hat k and vec r=(hat i-2hat j+hat k)beta+3hat k

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

Equation of the plane containing the lines vec r=(hat i-2hat j+hat k)+t(hat i+2hat j-hat k)vec r=(hat i+2hat j-hat k)+s(hat i+hat j+3hat k) is

If vec a=xhat i+yhat j+zhat k, then (widehat a xxhat i)*(hat i xxhat j)+(widehat a xxhat j)*(hat j xxhat k)+(widehat a xxhat k)*(hat k+hat i)

If vec a=3hat i-hat j-4hat k,vec b=2hat i+4hat j-3hat k and vec c=hat i+2hat j-widehat k, find |3vec a-2hat b+4hat c|