Find the angle between the lines r -3i-2j-4k- i-2j-2k and r - 5j-2k - 3i-2j-6k

The correct option is A #160;θ =cos ^ 1 ( 19 / 21 #160;) #160; #10; #10; #10; #10; #10; #10; #10; #10; #10; #10; #10; #10 ...

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Distance Formula

Find the angl...

Question

Find the angle between the lines $\to r = 3 i + 2 j - 4 k + λ (i + 2 j + 2 k)$ and $\to r = (5 j - 2 k) + μ (3 i + 2 j + 6 k)$

θ = {cos}^{- 1} (\frac{19}{21})

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θ = {sin}^{- 1} (\frac{19}{21})

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θ = {cos}^{- 1} (\frac{20}{21})

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None of these

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Solution

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\to r = 3 i + 2 j - 4 k + λ (i + 2 j + 2 k)

\to r = 5 i - 2 k + μ (3 i + 2 j + 6 k)

\vec{r} = (4 \hat{i} - \hat{j}) + λ (\hat{i} + 2 \hat{j} - 2 \hat{k}) and \vec{r} = \hat{i} - \hat{j} + 2 \hat{k} - μ (2 \hat{i} + 4 \hat{j} - 4 \hat{k})

\vec{r} = (3 \hat{i} + 2 \hat{j} - 4 \hat{k}) + λ (\hat{i} + 2 \hat{j} + 2 \hat{k}) and \vec{r} = (5 \hat{j} - 2 \hat{k}) + μ (3 \hat{i} + 2 \hat{j} + 6 \hat{k})

\vec{r} = λ (\hat{i} + \hat{j} + 2 \hat{k}) and \vec{r} = 2 \hat{j} + μ \{(\sqrt{3} - 1) \hat{i} - (\sqrt{3} + 1) \hat{j} + 4 \hat{k}\}

\vec{r} = 3 \hat{i} + 2 \hat{j} - 4 \hat{k} + λ (\hat{i} + 2 \hat{j} + 2 \hat{k}) and \vec{r} = 5 \hat{i} - 2 \hat{j} + μ (3 \hat{i} + 2 \hat{j} + 6 \hat{k})

\vec{r} = 3 \hat{i} + 8 \hat{j} + 3 \hat{k} + λ (3 \hat{i} - \hat{j} + \hat{k}) and \vec{r} = - 3 \hat{i} - 7 \hat{j} + 6 \hat{k} + μ (- 3 \hat{i} + 2 \hat{j} + 4 \hat{k})

\vec{r} = (3 \hat{i} + 5 \hat{j} + 7 \hat{k}) + λ (\hat{i} - 2 \hat{j} + 7 \hat{k}) and \vec{r} = - \hat{i} - \hat{j} - \hat{k} + μ (7 \hat{i} - 6 \hat{j} + \hat{k})

\vec{r} = (\hat{i} + 2 \hat{j} + 3 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) and \vec{r} = (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + μ (3 \hat{i} + 4 \hat{j} + 5 \hat{k})

\vec{r} = (1 - t) \hat{i} + (t - 2) \hat{j} + (3 - t) \hat{k} and \vec{r} = (s + 1) \hat{i} + (2 s - 1) \hat{j} - (2 s + 1) \hat{k}

\vec{r} = (λ - 1) \hat{i} + (λ + 1) \hat{j} - (1 + λ) \hat{k} and \vec{r} = (1 - μ) \hat{i} + (2 μ - 1) \hat{j} + (μ + 2) \hat{k}

\vec{r} = (2 \hat{i} - \hat{j} - \hat{k}) + λ (2 \hat{i} - 5 \hat{j} + 2 \hat{k}) and, \vec{r} = (\hat{i} + 2 \hat{j} + \hat{k}) + μ (\hat{i} - \hat{j} + \hat{k})

\vec{r} = (\hat{i} + \hat{j}) + λ (2 \hat{i} - \hat{j} + \hat{k}) and, \vec{r} = 2 \hat{i} + \hat{j} - \hat{k} + μ (3 \hat{i} - 5 \hat{j} + 2 \hat{k})

\vec{r} = (8 + 3 λ) \hat{i} - (9 + 16 λ) \hat{j} + (10 + 7 λ) \hat{k}

\vec{r} = 15 \hat{i} + 29 \hat{j} + 5 \hat{k} + μ (3 \hat{i} + 8 \hat{j} - 5 \hat{k})

\to r = (6 ˆ i + 2 ˆ j + 2 ˆ k) + λ (ˆ i - 2 ˆ j + 2 ˆ k)

\to r = (- 4 ˆ i - ˆ k) + μ (3 ˆ i - 2 ˆ j - 2 ˆ k)

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