Q.

The sine of the angle between the straight line x−23=y−34=z−45 and the plane 2x−2y+z=5 is

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answer is 0.14.

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Detailed Solution

Take (a1,b1,c1)=(3,4,5) and (a2,b2,c2)=(2,−2,1). Use cosπ2−θ=|a1a2+b1b2+c1c2|a 12+b 12+c 12a 22+b 22+c 22
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The sine of the angle between the straight line x−23=y−34=z−45 and the plane 2x−2y+z=5 is