If a, b, c and r are vectors such that a is n | vedclass

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(C) Given,$r 	imes b = c 	imes b$. This implies $(r - c) 	imes b = 0$. This means $(r - c)$ is parallel to $b$,so we can write $(r - c) = \lambda b

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$c - \frac{(c \cdot a)}{(b \cdot a)} b$

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(C) Given,$r 	imes b = c 	imes b$. This implies $(r - c) 	imes b = 0$. This means $(r - c)$ is parallel to $b$,so we can write $(r - c) = \lambda b$ for some scalar $\lambda$. Thus,$r = c + \lambda b$ ...$(i)$. We are also given $r \cdot a = 0$. Substituting $r$ from $(i)$,we get $(c + \lambda b) \cdot a = 0$. This expands to $c \cdot a + \lambda (b \cdot a) = 0$. Solving for $\lambda$,we get $\lambda = -\frac{c \cdot a}{b \cdot a}$ ...(ii). Substituting $\lambda$ back into equation $(i)$,we get $r = c - \left( \frac{c \cdot a}{b \cdot a} ight) b$.

If $a, b, c$ and $r$ are vectors such that $a$ is not perpendicular to $b$,$r \times b = c \times b$ and $r \cdot a = 0$,then $r =$

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