Find a - - b - xc- if a -2 i-jj-3 k- b -i -2 j-k- and c -3 ii-jj-2 k- - -CBSE 2014-

The given vectors are a #8594;=2i^+j^+3k^, #160;b #8594;= i^+2j^+k^ and c #8594;=3i^+j^+2k^. nbsp; Now, b #8594; #215;c #8594;=i^j^k^ 121312 ...

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Linear Combination of Vectors

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Question

Find $\vec{a} . (\vec{b} \times \vec{c})$ , if $\vec{a} = 2 \hat{i} + \hat{j} + 3 \hat{k}, \vec{b} = - \hat{i} + 2 \hat{j} + \hat{k}$ and $\vec{c} = 3 \hat{i} + \hat{j} + 2 \hat{k}$ . [CBSE 2014]

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\vec{a} = 3 \hat{i} - \hat{j} + 2 \hat{k}

\vec{b} = 2 \hat{i} + \hat{j} - \hat{k},

(\vec{a} \times \vec{b}) \vec{a} .

¯ ¯ ¯ a = ¯ i - 2 ¯ j + 3 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i + ¯ j + ¯ ¯ ¯ k, ¯ ¯ c = ¯ i + ¯ j + 2 ¯ ¯ ¯ k

∣ ∣ ∣ (\to a \times \to b) \times ¯ ¯ c ∣ ∣ ∣

∣ ∣ ∣ ¯ ¯ ¯ a \times (\to b \times \to c) ∣ ∣ ∣

\vec{a} = \hat{i} - \hat{j} + \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k}, \vec{c} = λ \hat{i} - \hat{j} + λ \hat{k}

\vec{a} = 2 \hat{i} - \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{c} = λ \hat{i} + λ \hat{j} + 5 \hat{k}

\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}, \vec{b} = 3 \hat{i} + λ \hat{j} + \hat{k}, \vec{c} = \hat{i} + 2 \hat{j} + 2 \hat{k}

\vec{a} = \hat{i} + 3 \hat{j}, \vec{b} = 5 \hat{k}, \vec{c} = λ \hat{i} - \hat{j}

[\vec{a} \vec{b} \vec{c}]

\vec{a} = 2 \hat{i} - 3 \hat{j}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and \vec{c} = 3 \hat{i} - \hat{k}

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} and \vec{c} = \hat{j} + \hat{k}

\vec{a} = 2 \hat{i} + 3 \hat{j} + \hat{k}, \vec{b} = \hat{i} - 2 \hat{j} + \hat{k} and \vec{c} = - 3 \hat{i} + \hat{j} + 2 \hat{k}

\to a = ˆ i - 3 ˆ k, \to b = 2 ˆ j - ˆ k, \to c = 2 ˆ i - 3 ˆ j + 2 ˆ k

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