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

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

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

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

Let A B C D be a parallelogram whose diagonals intersect at P and let O be the origin. Then prove that vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i+ hat j+ hat kdot

The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15a n d| vec r.( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,4) c. (-1,3,4) d. none of these

Statement 1: vec a=3 vec i+p vec j+3 vec k and vec b=2 vec i+3 vec j+q vec k are parallel vectors if p=9//2a n dq=2. Statement 2: if vec a=a_1 vec i+a_2 vec j+a_3 vec ka n d vec b=b_1 vec i+b_2 vec j+b_3 vec k are parallel, then (a_1)/(b_1)=(a_2)/(b_2)=(a_3)/(b_3)dot Which of the following Statements is/are correct ?

The ratio in which the plane vec rdot (vec i-2 vec j+3 vec k ) =17 divides the line joining the points -2 vec i+4 vec j+7 vec k and 3 vec i-5 vec j+8 vec k is a. 1:5 b. 1: 10 c. 3:5 d. 3: 10