The sine of the angle between the straight line `(x-2)/3=(y-3)/4=(z-4)/5` and the plane `2x-2y+z=5` isA. `10/(6sqrt(5))`B. `4/(5sqrt(2))`C. `(sqrt(2))/10`D. `(2sqrt(3))/5`

The sine of the angle between the straight line `(x-2)/3=(y-3)/4=(z-4)

1.	The sine of the angle between the straight line `(x-2)/3=(y-3)/4=(z-4)/5` and the plane `2x-2y+z=5` isA. `10/(6sqrt(5))`B. `4/(5sqrt(2))`C. `(sqrt(2))/10`D. `(2sqrt(3))/5`
Answer» Correct Answer - C The line is parallel to the vector `vecb=3hati+4hatj+5hatk` and the plane is normal to the vector `vecn=2hati-2hatj+hatk`. If `theta` is the angle between the line and the plane. Then `sin theta=(vecb.vecn)/(\|vecb\|\|vecn\|)impliessin theta=(6-8+5)/(sqrt(50)sqrt(9))=1/(5sqrt(2))=(sqrt(2))/10`

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The sine of the angle between the straight line `(x-2)/3=(y-3)/4=(z-4)/5` and the plane `2x-2y+z=5` isA. `10/(6sqrt(5))`B. `4/(5sqrt(2))`C. `(sqrt(2))/10`D. `(2sqrt(3))/5`

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