Question

Find the vector product of i+j+k and – 3i +j-2k
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Answer 1

Explanation:

Let → a = 3 ^ i + ^ j − ^ k a→=3i^+j^−k^ Read more on Sarthaks.com - https://www.sarthaks.com/719532/find-vector-product-of-vectors-3i-j-k-and-2i-3j-k

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Answer 2

${\orange{ \boxed{ \boxed{ \begin{array}{cc} \sf \: let, \\ \\ \sf \: \vec{a} = \hat{ i} + \hat{ j} + \hat{ k } \\ \\ \sf \vec{b} = - 3 \hat{i }+ \hat{j } - 2 \hat{k} \\ \\ \bf \: we \: have \: to \: find \: : \: \: \: \sf \vec{a} \times \vec{b}\end{array}}}}} \: \\ \\ \\ Now, \: \\ \\ \small{{ \begin{array}{cc} \sf \vec{a} \times \vec{b} = \begin{array}{ | ccc | } \sf \: \hat{i} \:& \sf\hat{j}& \sf \hat{k}\\ 1&1&1 \\ - 3&1& - 2 \: \end{array} \\ \\ \\ = \sf \: \hat{i} \{1 \times ( - 2) - 1 \times 1 \}- \hat{j} \{ - 2)\times 1 - 1 \times ( - 3) \}+ \hat{k} \{1 \times 1 - 1 \times ( - 3) \} \\ \\ \sf = \hat{i}( - 2 - 1) - \hat{j}( - 2 + 3 ) + \hat{k}(1 + 3) \\ \\ \sf = - 3 \hat{i} - \hat{j} + 4 \hat{k}\end{array} }}$