The coordinates of the point where the line `vec(r)=(6i-j-3k)+t(-i+4k)" meets the plane "vec(r)*(hat(i)+hat(j)-hat(k))=3` are

The position vectorof the point where the line vec(r)=hat(i)-hat(j)+hat(k)+t(hat(i)+hat(j)-hat(k)) meets the plane vec(r)*(hat(i)+hat(j)+hat(k))=5 , is

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

The angle between the lines vec(r)=(hat(i)+2hat(j)-3hat(k))+t(2hat(i)+hat(j)-2hat(k))" and the plane "vec(r)*(hat(i)+hat(j))+4=0 is

Find the angle between the line vec(r)=(2hat(i)-hat(j)+hat(k))+t(6hat(i)+2hat(j)-2hat(k))" and the plane "vec(r)*(6hat(i)+3hat(j)+2hat(k))=8

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

Find the point of intersection of the line : vec(r) = (hat(i) + 2 hat(j) + 3 hat(k) ) + lambda (2 hat(i) + hat(j) + 2 hat(k)) and the plane vec(r). (2 hat(i) - 6 hat(j) + 3 hat(k) ) + 5 = 0.