# If \vec{a}=2\hat{i}+3\hat{j}+4\hat{k} and \vec{b}=4\hat{i}-2\hat{j}+3\hat{k}. Find |\vec{a}×\vec{b}|.

Category: QuestionsIf \vec{a}=2\hat{i}+3\hat{j}+4\hat{k} and \vec{b}=4\hat{i}-2\hat{j}+3\hat{k}. Find |\vec{a}×\vec{b}|.
Editor">Editor Staff asked 11 months ago

If \vec{a}=2\hat{i}+3\hat{j}+4\hat{k} and \vec{b}=4\hat{i}-2\hat{j}+3\hat{k}. Find |\vec{a}×\vec{b}|.

(a) \sqrt{685}

(b) \sqrt{645}

(c) \sqrt{679}

(d) \sqrt{689}

The question was posed to me in an online quiz.

I want to ask this question from Product of Two Vectors-2 topic 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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Editor">Editor Staff answered 11 months ago

Correct choice is (b) \sqrt{645}

To explain: Given that, \vec{a}=2\hat{i}+3\hat{j}+4\hat{k} and \vec{b}=4\hat{i}-2\hat{j}+3\hat{k}

∴ \vec{a}×\vec{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\2&3&4\\4&-2&3\end{vmatrix}

=\hat{i}(9—8)-\hat{j}(6-16)+\hat{k}(-4-12)

=17\hat{i}+10\hat{j}-16\hat{k}

∴|\vec{a}×\vec{b}|=\sqrt{17^2+10^2+(-16)^2}

=\sqrt{289+100+256}

=\sqrt{645}