Let $ \vec{a}=\hat{i}-2 \hat{j}+\hat{k} $ and $ \vec{b}=\hat{i}-\hat{j}+\hat{k} $, be two vectors. If $ \vec{c} $, is a vector such that $ \vec{b} \times \vec{c}=\vec{b} \times \vec{a} $ and $ \vec{c} \cdot \vec{a}=0 $ then $ \vec{c} \cdot \vec{b} $, is equal to.

Question

Let $ \vec{a}=\hat{i}-2 \hat{j}+\hat{k} $ and $ \vec{b}=\hat{i}-\hat{j}+\hat{k} $, be two vectors. If $ \vec{c} $, is a vector such that $ \vec{b} \times \vec{c}=\vec{b} \times \vec{a} $ and $ \vec{c} \cdot \vec{a}=0 $ then $ \vec{c} \cdot \vec{b} $, is equal to., $ -\frac{3}{2} $, $ \frac{1}{2} $, $ -\frac{1}{2} $, $ -1 $

MARKS App · Accepted Answer

a → × b → × c → = a → × b → × a → ⇒ - a → . b → c → = a → . a → b → - a → . b → a → Using given information a → = i ^ - 2 j ^ + k ^ and b → = i ^ - j ^ + k ^ , we can write a → . b → = 4 , a → . a → = 6 ⇒ - 4 c → = 6 i ^ - j ^ + k ^ - 4 i ^ - 2 j ^ + k ^ ⇒ - 4 c → = 2 i ^ + 2 j ^ + 2 k ^ ⇒ c → = - 1 2 i ^ + j ^ + k ^ ⇒ b → . c → = - 1 2 .

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