Question

find the volume of the parallelepiped formed by the vectors 2i-3j+4k , i+2j-k and 3i-j+2k. Also find a vector of magnitude 11 and perpendicular to the plane formed by vectors, i+2j-k and 2i-3j+4k​

Answer 1

for volume we have to take scalar triple product of the vectors which represent the edges

so it comes out to be 37 cubic units

for perpendicular vector take cross product of the two given vectors

it comes out to be 5i-6j-7k

but its magnitude is not 11 so first find unit vector and then multiply it by 11

unit vector =5i-6j-7k/√110

our required vector =11/√110.(5i-6j-7k)