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The angle between the line $\bar{r} = (5 \bar{i} - \bar{j} - 4 \bar{k}) + λ (2 \bar{i} - \bar{j} + \bar{k})$ and the plane $\bar{r} . (3 \bar{i} - 4 \bar{j} - \bar{k}) + 5 = 0$ is

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detailed solution

Correct option is B

From the line (a1,b1,c1)=z,−1,1From the plane (a2,b2,c2)=(3,−4,−1)sinθ=|a1a2+b1b2+c1c2|a12+b12+c12a22+b22+c22

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The angle between the line r¯=(5i¯−j¯−4k¯)+λ(2i¯−j¯+k¯) and the plane r¯.(3i¯−4j¯−k¯)+5=0 is

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The angle between the line $\bar{r} = (5 \bar{i} - \bar{j} - 4 \bar{k}) + λ (2 \bar{i} - \bar{j} + \bar{k})$ and the plane $\bar{r} . (3 \bar{i} - 4 \bar{j} - \bar{k}) + 5 = 0$ is