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 the plane ` vec rdot( hat i+5 hat j+ hat k)=5` is a. `(10)/(3sqrt(3))` b. `(10)/9` c. `(10)/3` d. `3/(10)`

Find the angle between the line -> r=(2 hat i+3 hat j+9 hat k)+lambda(2 hat i+3 hat j+4 hat k) and the plane -> r(dot( hat i+ hat j+ hat k))=5.

Find the angle between the line vec r=(2hat i-hat j+3hat k)+lambda(3hat i-hat j+2hat k) and the plane vec r*(hat i+hat j+hat k)=3

The distance of the line vec r=2 hat i-2 hat j+3 hat k+lambda( hat i- hat j+4 hat k) from the plane vec rdot(( hat i+5 hat j+ hat k))=5, is 5/(3sqrt(3)) b. (10)/(3sqrt(3)) c. (25)/(3sqrt(3)) d. none of these

The distance of the point (-1, -5, -10) from the point of intersection of the line vec r=2 hat i- hat j+2 hat k+lambda(3 hat i+4 hat j+12 hat k) and the plane vec rdot(( hat i- hat j+ hat k)=5 is a. 9 b. 17 c. 13 d. none of these

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

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

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)+u(2hat i+4hat j-5hat 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 between (-1,-5,-10) from the point of intersection of the line vec r=2hat i-hat j+2hat k+lambda(3hat i+4hat j+2hat k) and the plane vec r*(hat i-hat j+hat k)=5

If line vec r=( hat i-2 hat j- hat k)+lambda(2 hat i+ hat j+2 hat k) is parallel to the plane vec r.(3 hat i-m hat k)=14 , then the value of m is (1). 2 (2) -2 (3) 0 (4) 3