[" 18.The coordinates of the point "P" on the line "],[vec r=(hat i+hat j+hat k)+lambda(-hat i+hat j-hat k)" which is nearest to the "],[" origin is "]

The coordinates of the point P on the line vec r=( hat i+ hat j+ hat k)+lambda(- hat i+ hat j- hat k) which is nearest to the origin is a. (2/4,4/3,2/3) b. (-2/3,-4/3,2/3) c. (2/3,-4/3,2/3) d. none of these

The coordinates of the point P on the line vec r=( hat i+ hat j+ hat k)+lambda(- hat i+ hat j- hat k) which is nearest to the origin is a. (2/4,4/3,2/3) b. (-2/3,-4/3,2/3) c. (2/3,-4/3,2/3) d. none of these

The coordinates of the point P on the line vec r=( hat i+ hat j+ hat k)+lambda(- hat i+ hat j- hat k) which is nearest to the origin is a. (2/4,4/3,2/3) b. (-2/3,-4/3,2/3) c. (2/3,-4/3,2/3) d. none of these

The coordinates of the point P on the line vec r=(hat i+hat j+hat k)+lambda(-hat i+hat j-hat k) which is nearest to the origin is a.((2)/(4),(4)/(3),(2)/(3)) b.(-(2)/(3),-(4)/(3),(2)/(3)) c.((2)/(3),-(4)/(3),(2)/(3)) d.none of these

The co-ordinate of the point P on the line r=(hat(i)+hat(j)+hat(k))+lambda(-hat(I)+hat(j)-hat(k)) which is nearest to the origin is

The co-ordinate of the point P on the line r=(hat(i)+hat(j)+hat(k))+lambda(-hat(I)+hat(j)-hat(k)) which is nearest to the origin is

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

The vector equation of the plane containing the line vec r=(-2 hat i-3 hat j+4 hat k)+lambda(3 hat i-2 hat j- hat k) and the point hat i+2 hat j+3 hat k is a. vec rdot(( hat i+3 hat k)=10 b. vec rdot(( hat i-3 hat k)=10 c. vec rdot((3 hat i+ hat k)=10 d. none of these

The vector equation of the plane containing the line vec r=(-2 hat i-3 hat j+4 hat k)+lambda(3 hat i-2 hat j- hat k) and the point hat i+2 hat j+3 hat k is a. vec rdot(( hat i+3 hat k)=10 b. vec rdot(( hat i-3 hat k)=10 c. vec rdot((3 hat i+ hat k)=10 d. none of these

Find the angle between the line vec r=hat i+2hat j-hat k+lambda(hat i-hat j+hat k) and the plane vec r*(2hat i-hat j+hat k)=4