If a line has a vector equation `vec r=2hat i+6hat j+lambda (hat i-3hat j)`,then which of the following statements(s) is/are NOY correct?

Consider the following 3 lines in space L_1: vec r= 3hat i-hat j+ 2hat k + lambda(2hat i + 4hat j-hat k) , L_2 :vec r =hat i+hat j- 3hat k + mu(4hat i + 2hat j+ 4hat k) and L_3 : vec r = 3hat i+2hat j- 2hat k + t(2hat i+hat j+ 2hat k) Then which one of the following pair(s) are in the same plane.

Image of the point P with position vector 7hat i-hat j+2hat k in the line whose vector equation is,vec r=9hat i+5hat j+5hat k+lambda(hat i+3hat j+5hat k) has the position vector

Find the shortest distance between the lines whose vector equations are vec r=(hat i+2hat j+3hat k)+lambda(hat i-3hat j+2hat k) and vec r=4hat i+5hat j+6hat k+mu(2hat i+3hat j+hat k)

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

Vector equation of the plane r=hat i-hat j+lambda(hat i+hat j+hat k)+mu(hat i2hat j+3hat k) in the scalar dot product form is

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

Image of the point P with position vector 7hat(i) - hat(j) + 2hat(k) in the line whose vector equation is vec(r) = 9hat(i) + 5hat(j) + 5hat(k) + lambda(hat(i) + 3hat(j) + 5hat(k)) has the position .