JEE Main On 8 April 2017 Question 5
Question: The area (in sq. units) of the parallelogram whooshed diagonals are along the vectors $ 8\hat{i}-6\hat{j} $ and $ 3\hat{i}+4\hat{j}-12\hat{k}, $ is: [JEE Online 08-04-2017]
Options:
A) 20
B) 65
C) 52
D) 26
Show Answer
Answer:
Correct Answer: B
Solution:
$ d _1\times d _2= \begin{vmatrix} i & j & k \\ 8 & -6 & 0 \\ 3 & 4 & -12 \\ \end{vmatrix} $
$ =72\hat{i}-(-96)\hat{j}+50\hat{k} $
$ =5178+7056+2500 $
$ |d _1\times d _2|=\sqrt{16900}=130 $
$ A=\frac{1}{2}|d _1\times d _2|=\frac{1}{2}\times 130 $ = 65
