(i) Let a →=i^+4j^+2k^, b →=3i^-2j^+7k^ and c →=2i^-j^+4k^. Find a vector d →which is perpendicular to both a →and b →and c →·d →=15.(ii) Let a→=4i^+5j^-k^, b→=i^-4j^+5k^ and c→=3i^+j^-k^. Find a vector d → which is perpendicular to both c→ and b→ and d→.a→=21.

(i) Let a →=i^+4j^+2k^, b →=3i^-2j^+7k^ and c →=2i^-j^+4k^. Find

1.	(i) Let a →=i^+4j^+2k^, b →=3i^-2j^+7k^ and c →=2i^-j^+4k^. Find a vector d →which is perpendicular to both a →and b →and c →·d →=15.(ii) Let a→=4i^+5j^-k^, b→=i^-4j^+5k^ and c→=3i^+j^-k^. Find a vector d → which is perpendicular to both c→ and b→ and d→.a→=21.
Answer» (i) Let $\vec{a} = \hat{i} + 4 \hat{j} + 2 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + 7 \hat{k} and \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .$ Find a vector $\vec{d}$ which is perpendicular to both $\vec{a} and \vec{b}$ $and \vec{c} \cdot \vec{d} = 15 .$ (ii) Let $\vec{a} = 4 \hat{i} + 5 \hat{j} - \hat{k}, \vec{b} = \hat{i} - 4 \hat{j} + 5 \hat{k} and \vec{c} = 3 \hat{i} + \hat{j} - \hat{k}$ . Find a vector $\vec{d}$ which is perpendicular to both $\vec{c} and \vec{b} and \vec{d} . \vec{a} = 21$ .