Let a→, b→ and c→ be three non - coplanar unit vectors such that the angle between every pair of them is (π)/3. If a→ × b→+ b→ × c→=pa→+qb→+rc→…

Question

Let a→, b→ and c→ be three non - coplanar unit vectors such that the angle between every pair of them is (π)/3. If a→ × b→+ b→ × c→=pa→+qb→+rc→ , where p, q and r are scalars, then the value of (p^2+2q^2+r^2)/(q^2) is _______

MARKS Content Team · Accepted Answer

Correct answer: 4. a→=b→= c→=1 a→ × b→+ b→ × c→=pa→+qb→+rc→ a→ . b→ × c→=p+q a→ . b→+ra→ . c→ And a→ b→ c→=1/(√2) p+q/2+r/2=a→ b→ c→ .......(i) p/2+q+r/2=0 ......(ii) p/2+q/2+r=a→ b→ c→ ......(iii) ⇒ p=r= -q (p^2+2q^2+r^2)/(q^2)=4

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Let a→, b→ and c→ be three non - coplanar unit vectors such that the angle between every pair of them is π3. If a→ × b→+ b→ × c→=pa→+qb→+rc→ , where p, q and r are scalars, then the value of p2+2q2+r2q2 is _______

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