A vector,c→ directed along the internal $$bi-sector$$ of the angle between the vectors a→$$=7i^$$−$$4j^$$−$$4k^$$ and b→$$=$$−$$2i^-j^+2k^$$, with |c→|$$=56$$, is

Question

A vector,c→ directed along the internal $$bi-sector$$ of the angle between the   vectors a→$$=7i^$$−$$4j^$$−$$4k^$$ and b→$$=$$−$$2i^-j^+2k^$$, with |c→|$$=56$$, is

Infinity Learn · Accepted Answer

The required vectors c→ is given by λa→a→$$+b$$→b→now a→a→$$=197i^$$−$$4j^$$−$$4k^$$ and b→b→$$=13$$−$$2i^-j^+2k^$$⇒          c→$$=$$λ$$19i^$$−$$79j^+29k^$$⇒c→$$2=$$λ$$2$$×$$5481$$ Therefore, λ$$2=225$$ or λ$$=$$±$$15$$⇒                                                                     c→$$=$$±$$53i^$$−$$7j^+2k^$$

$A vector, \vec{c} directed along the internal bi-sector of the angle between the vectors \vec{a} = 7 \hat{i} - 4 \hat{j} - 4 \hat{k} and \vec{b} = - 2 \hat{i} - \hat{j} + 2 \hat{k}, with | \vec{c} | = 5 \sqrt{6}, is$

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A vector,c→ directed along the internal bi-sector of the angle between the vectors a→=7i^−4j^−4k^ and b→=−2i^-j^+2k^, with |c→|=56, is

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$A vector, \vec{c} directed along the internal bi-sector of the angle between the vectors \vec{a} = 7 \hat{i} - 4 \hat{j} - 4 \hat{k} and \vec{b} = - 2 \hat{i} - \hat{j} + 2 \hat{k}, with | \vec{c} | = 5 \sqrt{6}, is$