If a, b are two non-zero vectors and c is nonzero scalar, and a·r=c, a×r=b then r=

a×r=b ⇒ a×(a×r)=a×b ⇒ (a·r) a-|a|2 r=a×b ⇒ c a-a×b=|a|2 r ⇒ r=c|a|2 a-a×b|a|2

If a, b are two non-zero vectors and c is nonzero scalar, and a·r=c, a×r=b then r=

a×r=b ⇒ a×(a×r)=a×b ⇒ (a·r) a-|a|2 r=a×b ⇒ c a-a×b=|a|2 r ⇒ r=c|a|2 a-a×b|a|2

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If $a, b$ are two non-zero vectors and c is nonzero scalar, and $a \cdot r = c, a \times r = b$ then $r =$

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$\frac{a}{{|a|}^{2}} - c \frac{a \times b}{{|a|}^{2}}$

$a - a \times b$

$c a - (a \times b)$

$\frac{c a}{{|a|}^{2}} - \frac{a \times b}{{|a|}^{2}}$

answer is B.

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Detailed Solution

$a \times r = b \Rightarrow a \times (a \times r) = a \times b \Rightarrow (a \cdot r) a - | a |^{2} r = a \times b \Rightarrow c a - a \times b = | a |^{2} r \Rightarrow r = \frac{c}{| a |^{2}} a - \frac{a \times b}{| a |^{2}}$

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