If a -2i-j-3k and b-i-4k then- find -a -b-

The correct option is A √(3) a =2i+j 3k b =i 4k Therefore, a b = i+j+k Thus, |a b|=√(1+1+1)=√(3) ...

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Addition and Subtraction of Surds

If a =2i+j-...

Question

If $\to a = 2 ˆ i + ˆ j - 3 ˆ k$ and $\to b = ˆ i - 4 ˆ k$ then, find $| \to a - \to b |$ .

\sqrt{3}

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\sqrt{2}

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\sqrt{5}

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2 \sqrt{5}

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Solution

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a = 3 i + 3 j + 4 k, b = i + j + k

c = 4 i + 2 j + 3 k

\frac{1}{5 \sqrt{2}} | a \times (b \times c) |

If \vec{a} = 3 \hat{i} - \hat{j} - 4 \hat{k}, \vec{b} = - 2 \hat{i} + 4 \hat{j} - 3 \hat{k} and \vec{c} = \hat{i} + 2 \hat{j} - \hat{k}, find |3 \vec{a} - 2 \vec{b} + 4 \vec{c}| .

¯ ¯ ¯ a = 2 ˆ i - ˆ j + ˆ k

¯ ¯ b = ˆ i + ˆ j + 3 ˆ k

¯ ¯ ¯ a \times ¯ ¯ b

∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣

\to a = 2 i - j + k

\to b = i - 2 j + 4 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) ∣ ∣ ∣

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