Find the projection of b - c - on a - where a -2 i -2 j - k - b - i -2 j -2 k - and c -2 i - j -4 k -

Given #160;thata #8594;=2i^ 2j^+k^b #8594;=i^+2j^ 2k^and #160;c #8594;=2i^ j^+4k^ #8756; #160;b #8594;+c #8594;=i^+2j^ 2k^+2i^ j^+4k^=3i^+j^+2 ...

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(x±a)(x±b) = x²±(a+b)x+ab.

Find the proj...

Question

Find the projection of $\vec{b} + \vec{c} on \vec{a}$ , where $\vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} and \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .$

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\vec{b} + \vec{c} on \vec{a} when \vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} and \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .

\vec{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} + 2 \hat{k}

\vec{a} = 2 \hat{i} - 3 \hat{j} + 4 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{c} = 3 \hat{i} - \hat{j} - 2 \hat{k}

\vec{a} = 11 \hat{i}, \vec{b} = 2 \hat{j}, \vec{c} = 13 \hat{k}

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

[\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}

¯ ¯ ¯ 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) ∣ ∣ ∣

∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣

\to a = 2 i - j + k

\to b = i - 2 j + 4 k

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