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Algebra

Please tell above answer quickly and as soon as possible with proper explanation

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Profile image of Anvita Mahajan
7 Years agoGrade
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1 Answer

Profile image of Samyak Jain
7 Years ago
Given : a and b are not perpendicular to each other or a.b = 0r x a = b x a   ...(1),  r.c = 0.
Cross product both sides of (1) with c. So,
(r x a) x c = (b x a) x c  \Rightarrow  (r.c)a – (a.c)r = (b.c)a – (a.c)b  ...by using definition of vector triple product.
\Rightarrow  – (a.c)r = (b.c)a – (a.c)b              [Given : r.c = 0]
r = – { (b.c)/(a.c) } a + { (a.c)/(a.c) }b 
r = b – { (b.c)/(a.c) } a .