If a - 2i - j - 5 k and b - 4 i - 2 j - -k such that a - b- find the value of -

If A⃗ = a = 2i j + 5 k B⃗ = #160;b = 4 i 2 j + λk #160;We know that: #160;a ∥ #160;b ,Therefore, B⃗= kA⃗ Here, by observation, ...

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Definition of Parallel Lines

If a = 2i -...

Question

If $\to a = 2 ˆ i - ˆ j + 5 ˆ k$ and $\to b = 4 ˆ i - 2 ˆ j + λ ˆ k$ such that $\to a | | \to b$ , find the value of $λ$ .

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\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}

a = 2 i - j + k, b = i + 2 j - 3 k, c = 3 i + λ j + 5 k

λ

\vec{a} and \vec{b}

\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 4 \hat{i} - 9 \hat{j} + 2 \hat{k}

\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 5 \hat{i} - 9 \hat{j} + 2 \hat{k}

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

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

3 ¯ i - 2 ¯ j - ¯ ¯ ¯ k, 2 ¯ i + 3 ¯ j - 4 ¯ ¯ ¯ k, - ¯ i + ¯ j + 2 ¯ ¯ ¯ k

4 ¯ i + 5 ¯ j + λ ¯ ¯ ¯ k

λ = \frac{- 146}{m}

m

¯ ¯ ¯ a = ¯ i + 2 ¯ j, ¯ ¯ b = - 2 ¯ i + ¯ j, ¯ ¯ c = 4 ¯ i + 3 ¯ j

x

y

¯ ¯ c = x ¯ ¯ ¯ a + y ¯ ¯ b

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