If A→$$=2i^+3j^+6k^$$ andB→$$=3i^$$−$$6j^+2k^$$ , then vector perpendicular to both A→ and B→ has magnitude k times that $$of(6i^+2j^$$−$$3k^)$$ . Then k is equal to

Question

If  A→$$=2i^+3j^+6k^$$      andB→$$=3i^$$−$$6j^+2k^$$     , then vector perpendicular to both A→      and B→      has magnitude k  times that $$of(6i^+2j^$$−$$3k^)$$     . Then k is equal to

Infinity Learn · Accepted Answer

Let C→  be a vector perpendicular to A→  and B→ Then as per question kC→$$=A$$→×B→or   $$k=(A$$→×B→$$)C$$→          $$=(2i^+3j^+6k^)$$×(3i^$$−$$6j^+2k^)(6i^+2j^$$−$$3k^)         $$=(42i^+14j^$$−$$21k^)(6i^+2j^$$−$$3k^)=7$$∵$$i^$$×$$i^=j^$$×$$j^=k^$$×$$k^=0$$ $$i^$$×$$j^=k^$$     $$j^$$×$$k^=i^$$   $$k^$$×$$i^=j^$$

If $\vec{A} = 2 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\vec{B} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k}$ , then vector perpendicular to both $\vec{A}$ and $\vec{B}$ has magnitude k times that of $(6 \hat{i} + 2 \hat{j} - 3 \hat{k})$ . Then k is equal to

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If A→=2i^+3j^+6k^ andB→=3i^−6j^+2k^ , then vector perpendicular to both A→ and B→ has magnitude k times that of(6i^+2j^−3k^) . Then k is equal to

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If $\vec{A} = 2 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\vec{B} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k}$ , then vector perpendicular to both $\vec{A}$ and $\vec{B}$ has magnitude k times that of $(6 \hat{i} + 2 \hat{j} - 3 \hat{k})$ . Then k is equal to