Find a-b - c-d if a - i - j - k- b - 2i - k- c - 2i - j - k and d - i - j - 2k-

#160;a × #160;b = i #160; amp; j #160; amp;k #160; 1 #160; amp; 1 amp; 1 2 #160; amp; 0 amp; 1 = i(1) j (1 2) ...

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Applications of Cross Product

Find a×b . ...

Question

Find $(\to a \times \to b) . (\to c \times \to d)$ if $\to a = \to i + \to j + \to k, \to b = 2 \to i + \to k, \to c = 2 \to i + \to j + \to k$ and $\to d = \to i + \to j + 2 \to k$ .

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[\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}

\vec{a} and \vec{b}

\vec{a} = \hat{i} - \hat{j} and \vec{b} = \hat{j} + \hat{k}

\vec{a} = 3 \hat{i} - 2 \hat{j} - 6 \hat{k} and \vec{b} = 4 \hat{i} - \hat{j} + 8 \hat{k}

\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k} and \vec{b} = 4 \hat{i} + 4 \hat{j} - 2 \hat{k}

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

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

¯ ¯ ¯ 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} = 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}

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