If a→=1,-1,2,b→=-2,3,5,c→=2,-2,4 and i^ is the unit vector in the x -direction, then a→-2b→+3c→i^=

a→=1,−1,2,b→=−2,3,5,c→=2,−2,4So,a→=1,−1,2≡i^−j^+2k^;b^=−2,3,5≡−2i^+3j^+5k^and c→=2,−2,4≡2i^−2j^+4k^⇒a→−2b→+3c→=i^−j^+2k^−2−2k^+3j^+5k^+32i^−2j^+4k^=11i^−13j^+4k^ and a→−2b→+3ci^=11

If a→=1,-1,2,b→=-2,3,5,c→=2,-2,4 and i^ is the unit vector in the x -direction, then a→-2b→+3c→i^=

a→=1,−1,2,b→=−2,3,5,c→=2,−2,4So,a→=1,−1,2≡i^−j^+2k^;b^=−2,3,5≡−2i^+3j^+5k^and c→=2,−2,4≡2i^−2j^+4k^⇒a→−2b→+3c→=i^−j^+2k^−2−2k^+3j^+5k^+32i^−2j^+4k^=11i^−13j^+4k^ and a→−2b→+3ci^=11

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$If \vec{a} = (1, - 1, 2), \vec{b} = (- 2, 3, 5),$ $\vec{c} = (2, - 2, 4) and \hat{i} is the unit$ $vector in the x -direction, then$ $(\vec{a} - 2 \vec{b} + 3 \vec{c}) \hat{i} =$

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Detailed Solution

$\begin{array}{l} \vec{a} = (1, - 1, 2), \vec{b} = (- 2, 3, 5), \vec{c} = (2, - 2, 4) \\ S o, \vec{a} = (1, - 1, 2) \equiv \hat{i} - \hat{j} + 2 \hat{k}; \hat{b} = (- 2, 3, 5) \equiv - 2 \hat{i} + 3 \hat{j} + 5 \hat{k} \\ a n d \vec{c} = (2, - 2, 4) \equiv 2 \hat{i} - 2 \hat{j} + 4 \hat{k} \\ \Rightarrow \vec{a} - 2 \vec{b} + 3 \vec{c} = (\hat{i} - \hat{j} + 2 \hat{k}) - 2 (- 2 \hat{k} + 3 \hat{j} + 5 \hat{k}) + 3 (2 \hat{i} - 2 \hat{j} + 4 \hat{k}) \\ = 11 \hat{i} - 13 \hat{j} + 4 \hat{k} a n d (\vec{a} - 2 \vec{b} + 3 c) \hat{i} = 11 \end{array}$