Find the vector product of the vectors \vec{a}=-\hat{j}+\hat{k} and \vec{b}=-\hat{i}-\hat{j}-\hat{k}.

Category: QuestionsFind the vector product of the vectors \vec{a}=-\hat{j}+\hat{k} and \vec{b}=-\hat{i}-\hat{j}-\hat{k}.
Editor">Editor Staff asked 11 months ago

Find the vector product of the vectors \vec{a}=-\hat{j}+\hat{k} and \vec{b}=-\hat{i}-\hat{j}-\hat{k}.
 
(a) 2\hat{i}-\hat{j}+\hat{k}
 
(b) 2\hat{i}-\hat{j}-4\hat{k}
 
(c) \hat{i}+\hat{j}-\hat{k}
 
(d) 2\hat{i}-\hat{j}-\hat{k}
 
The question was asked in examination.
 
Query is from Product of Two Vectors-2 in division Vector Algebra of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

The correct choice is (d) 2\hat{i}-\hat{j}-\hat{k}
 
To elaborate: Given that, \vec{a}=-\hat{j}+\hat{k} and \vec{b}=-\hat{i}-\hat{j}-\hat{k}
 
Calculating the vector product, we get
 
\vec{a}×\vec{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\0&-1&1\\-1&-1&-1\end{vmatrix}
 
=\hat{i}(1-(-1))-\hat{j}(0-(-1))+\hat{k}(0-1)
 
=2\hat{i}-\hat{j}-\hat{k}