Question

Find the scalar and vector products of two vectors a = (2i – 3j^ + 4k) and b = (î – 2j +3k).​

Answer 1

SoluTion:

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Given -

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• $\sf{\vec{a}}$ = $\sf{2 \hat{i} - 3 \hat{j} + 4 \hat{k}}$

• $\sf{\vec{b}}$ = $\sf{\hat{i} - 2 \hat{j} + 3 \hat{k}}$

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Scaler product -

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$\sf{\vec{a}.\vec{b}}$ = $\sf{\bigg(2 \hat{i} - 3 \hat{j} + 4 \hat{k}\bigg).}$ $\sf{\bigg(\hat{i} - 2 \hat{j} + 3 \hat{k}\bigg)}$

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$\longrightarrow$ $\sf{\vec{a}.\vec{b}}$ = $\sf{2+6+12}$ ⠀⠀⠀⠀⠀⠀⠀⠀

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$\longrightarrow$ $\sf{\vec{a}.\vec{b}}$ = $\sf{20}$

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Vector product -

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$\sf{\vec{a} \times \vec{b} =}{\left| \begin{tabular}{ccc} \sf \hat{i} & \sf \hat{j} & \sf \hat{k} \\ \sf 2 & \sf -3 & \sf 4 \\ \sf 1 & \sf -2 & \sf 3\end{tabular} \right|}$

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$\longrightarrow$ $\sf{\vec{a} \times \vec{b}}$ = $\sf{\hat{i} ( -9 + 8) - \hat{j} (6-4) + \hat{k} (-4+3)}$

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$\longrightarrow$ $\sf{\vec{a} \times \vec{b}}$ = $\sf{ - \hat{i} - 2 \hat{j} - \hat{k}}$