The volume of he parallelepiped whose sides are given by ` vec O A=2i-2, j , vec O B=i+j-ka n d vec O C=3i-k` is a.`4/13` b. `4` c. `2/7` d. `2`

Find the altitude of a parallelepiped whose three coterminous edtges are vectors vec A= hat i+ hat j+ hat k , vec B=2 hat i+4 hat j- hat ka n d vec C= hat i+ hat j+3 hat kw i t h vec Aa n d vec B as the sides of the base of the parallepiped.

Find the volume of a parallelopiped whose edges are represented by the vectors vec a = 2 hat i -3 hat j -4 hat k and vec b = hat i +2 hat j - hat k and vec c = 3 hat i + hat j + 2 hat k .

Find the volumes of the following parapllelopipeds whose three co - terminus edges are (i) vec a = 2 hat i - 3 hat j + 4 hat k, vec b = 3 hat i - hatj + 2 hat k and vec c = hat i + 2 hat j - hat k . (ii) vec a = hat i - 2 hat j + 3 hat k, vec b = 2hat i + hat j - hat k and vec c = 2 hat i + hat j - hat k .

Let vec P R=3 hat i+ hat j-2 hat ka n d vec S Q= hat i-3 hat j-4 hat k determine diagonals of a parallelogram P Q R S ,a n d vec P T= hat i+2 hat j+3 hat k be another vector. Then the volume of the parallelepiped determine by the vectors vec P T , vec P Q and vec P S is 5 b. 20 c. 10 d. 30

Find the area of the parallelogram whose adjacent sides are determined by the vectors vec a= hat i- hat j+3 hat ka n d vec b=2 hat i-7 hat j+ hat kdot

Find the area of a parallelogram whose adjacent sides are determined by the vectors vec a = 2 hat i - hat j +3 hat k and vec b = hat i- 6 hat j+ 4 hat k is

Find the area of the parallelogram whose adjacent sides are determined by the vectors vec a = hat i - hat j + 3 hat k and vec b = 2 hat i - 7 hat j + hat k .

Find the area a parallelogram whose diagonals are vec a=3 hat i+ hat j-2 hat ka n d vec b= hat i-3 hat j+4 hat kdot

If vec a^'= hat i+ hat j , vec b^'= hat i- hat j+2 hat k and vec c^' = 2 hat i+ hat j- hat k , then the altitude of the parallelepiped formed by the vectors vec a , vec b and vec c having base formed by vec b and vec c is (where vec a ' is reciprocal vector vec a )

Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja n d vec c=-2 hat i+21 hat j such that vecalpha= vec a+ vec b+ vec c Then the resolution of the vector vecalpha into components with respect to vec aa n d vec b is given by a. 3 vec a-2 vec b b. 3 vec b-2 vec a c. 2 vec a-3 vec b d. vec a-2 vec b