Q.

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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a

sin−15291

b

sin−19156

c

sin−15156

d

sin−1956

answer is B.

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Detailed Solution

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