If a→$$=5i^$$−$$j^+k^$$,b→$$=2i^$$−$$3j^$$−$$k^$$,c→$$=$$−$$3i^+j^+k^$$ and d→$$=2j^+k^$$, then the value of d→⋅(a$$→×$${b$$→×$$(c$$→×d→$$)}) equals

Question

If a→$$=5i^$$−$$j^+k^$$,b→$$=2i^$$−$$3j^$$−$$k^$$,c→$$=$$−$$3i^+j^+k^$$ and d→$$=2j^+k^$$, then  the value of d→⋅(a$$→×$${b$$→×$$(c$$→×d→$$)}) equals

Infinity Learn · Accepted Answer

Given vectors are a→$$=5i^$$−$$j^+k^$$,b→$$=2i^$$−$$3j^$$−$$k^$$,c→$$=$$−$$3i^+j^+k^$$ and d→$$=2j^+k^$$ We have a→×(b$$→×c→$$)=(a$$→⋅c→$$)b$$→−$$(a$$→⋅b→$$)c$$→ Here b→⋅d→$$=$$−$$7$$ and b→⋅c→$$=$$−$$10$$ Now, b→×$$(c$$→×d→$$)=(b$$→⋅d→$$)c$$→−$$(b$$→⋅c→$$)d$$→$$=$$−$$7c$$→$$+10d$$→a→×$$(b$$→×$$(c$$→×d→$$))=a$$→×$$(10d$$→−$$7c$$→$$)=10a$$→×d→−$$7a$$→×c→ Now, d→⋅$$(a$$→×$$(b$$→×$$(c$$→×d→$$)))=d$$→⋅$$(10a$$→×d→−$$7a$$→×c→$$)=10$$[d→a→d→]−$$7$$[d→ a→c→]$$=10(0)−$$70215$$−$$11$$−$$311=$$−$$7$$[$$0$$−$$2(5+3)+1(5$$−$$3)$$]$$=98Therefore$$, the correct answer is (1).

$If \vec{a} = 5 \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} - 3 \hat{j} - \hat{k}, \vec{c} = - 3 \hat{i} + \hat{j} + \hat{k} and \vec{d} = 2 \hat{j} + \hat{k}, then the value of \vec{d} \cdot (\vec{a} \times {\vec{b} \times (\vec{c} \times \vec{d})}) equals$

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If a→=5i^−j^+k^,b→=2i^−3j^−k^,c→=−3i^+j^+k^ and d→=2j^+k^, then the value of d→⋅(a→×{b→×(c→×d→)}) equals

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$If \vec{a} = 5 \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} - 3 \hat{j} - \hat{k}, \vec{c} = - 3 \hat{i} + \hat{j} + \hat{k} and \vec{d} = 2 \hat{j} + \hat{k}, then the value of \vec{d} \cdot (\vec{a} \times {\vec{b} \times (\vec{c} \times \vec{d})}) equals$