The angle between planes r¯.2i¯−3j¯+4k¯+11=0 and r¯.3i¯−2j¯−3k¯+27=0 is

n¯1.n¯2n¯1n¯2=cosθ⇒2i¯−3j¯+4k¯3i¯−2j¯−3k¯22+−32+4232+−22+−32=cosθ⇒cosθ=6+6−122922=02922=0⇒θ=90

The angle between planes r¯.2i¯−3j¯+4k¯+11=0 and r¯.3i¯−2j¯−3k¯+27=0 is

n¯1.n¯2n¯1n¯2=cosθ⇒2i¯−3j¯+4k¯3i¯−2j¯−3k¯22+−32+4232+−22+−32=cosθ⇒cosθ=6+6−122922=02922=0⇒θ=90

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The angle between planes $\bar{r} . (2 \bar{i} - 3 \bar{j} + 4 \bar{k}) + 11 = 0$ and $\bar{r} . (3 \bar{i} - 2 \bar{j} - 3 \bar{k}) + 27 = 0$ is

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$\frac{π}{6}$

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{2}$

answer is D.

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$\frac{{\bar{n}}_{1} . {\bar{n}}_{2}}{|{\bar{n}}_{1}| |{\bar{n}}_{2}|} = \cos θ$

$\Rightarrow \frac{(2 \bar{i} - 3 \bar{j} + 4 \bar{k}) (3 \bar{i} - 2 \bar{j} - 3 \bar{k})}{\sqrt{{(2)}^{2} + {(- 3)}^{2} + {(4)}^{2}} \sqrt{{(3)}^{2} + {(- 2)}^{2} + {(- 3)}^{2}}} = \cos θ$

$\Rightarrow \cos θ = \frac{6 + 6 - 12}{\sqrt{29} \sqrt{22}} = \frac{0}{\sqrt{29} \sqrt{22}} = 0 \Rightarrow θ = 90$

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The angle between planes r¯.2i¯−3j¯+4k¯+11=0 and r¯.3i¯−2j¯−3k¯+27=0 is

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The angle between planes $\bar{r} . (2 \bar{i} - 3 \bar{j} + 4 \bar{k}) + 11 = 0$ and $\bar{r} . (3 \bar{i} - 2 \bar{j} - 3 \bar{k}) + 27 = 0$ is