[" 16.दश्राड्टा कि स्सदिश "2hat i-3hat j+4hat k" और "-4hat i+6j-],[" हें "1]

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.

find the projection of 3hat i - hat j + 4hat k on 2 hat i + 3 hat j -6 hat k

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i-3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j-2hat k

Find the area of the parallelogram determined by the vectors: 2hat i and 3hat j2hat i+hat j+3hat k and hat i-hat j3hat i+hat j-2hat k and hat i-3hat j+4hat khat i-3hat j+hat k and hat i+hat j+hat k

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

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

underset with a = 2hat i + hat j-3hat k, vec b = -hat i + hat j + 2hat k, vec c = 4hat i + 3hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i+3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j+2hat k

Show that the points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k