Find the acute angle between the planes r - i -2 j -2 k -1 and r - 3 i -6 j -2 k -0-

For given plane r #8594;.i^ 2j^ 2k^=1 #160;and #160;r #8594;.3i^ 6j^+2k^=0Using #160;formula #160;for #160;plane #160;r #8594;.n #8594;1=d1 ...

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Angle between Two Planes

Find the acut...

Question

Find the acute angle between the planes $\vec{r} \cdot (\hat{i} - 2 \hat{j} - 2 \hat{k}) = 1 and \vec{r} \cdot (3 \hat{i} - 6 \hat{j} + 2 \hat{k})$ = 0.

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

\vec{r} \cdot (2 \hat{i} - \hat{j} + 2 \hat{k}) = 6 and \vec{r} \cdot (3 \hat{i} + 6 \hat{j} - 2 \hat{k}) = 9

\vec{r} \cdot (2 \hat{i} + 3 \hat{j} - 6 \hat{k}) = 5 and \vec{r} \cdot (\hat{i} - 2 \hat{j} + 2 \hat{k}) = 9

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

\to r . (3 \to i - 2 \to j + 6 \to k) = 0

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

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

\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}\}

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