hat j-hat k+mu(3hat i-5hat j

Find the angle between the following pairs of lines: (i) quad vec r=2hat i-5hat j+hat k+lambda(3hat i+2hat j+6hat k) and vec r=3hat i+hat j-2hat k+lambda(hat i-hat j-2hat k)vec r=3hat i+hat j-26hat k+mu(3hat i-5hat j-2hat k)

Find the shortest distance between the lines whose vector equations are 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)dot

Find the shortest distance between the lines 11 and 12 whose vector equations are quad vec r=hat i+hat j+lambda(2hat i-hat j+hat k) (1) and quad vec r=2hat i+hat j-k+mu(3hat i-5hat j+2hat k)

Find the shortest distance between the lines l1 and l2 whose vector equations are -> r= hat i+ hat j+lambda(2 hat i- hat j+ hat k) (1)and -> r=2 hat i+ hat j-k+mu(3 hat i-5 hat j+2 hat k) (2)

Find the shortest distance between the lines l1 and l2 whose vector equations are vecr= hat i+ hat j+lambda(2 hat i- hat j+ hat k) (1)and vecr=2 hat i+ hat j-k+mu(3 hat i-5 hat j+2 hat k) (2)

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

Find the value of (3hat i-hat j+5hat k)-(hat i-5hat j+3hat k)

Find the vector and cartesian equation of a plane containing the two lines vec r=(2hat i+hat j-3hat k)+lambda(hat i+2hat j+5hat k) and vec r=(3hat i+3hat j+2hat k)+mu(3hat i-2hat j+5hat k) Also,show that the line vec r=(2hat i+5hat j+2hat k)+P(3hat i-2hat j+5hat k) lies in the plane.

If vec r=(hat i+2hat j+3hat k)+lambda(hat i-hat j+hat k) and vec r=(hat i+2hat j+3hat k)+mu(hat i+hat j-hat k) are bisector of two lines is

Prove that point hat i+2hat j-3hat k,2hat i-hat j+hat k and 2hat i+5hat j-hat k from a triangle in space.