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प्रश्न
The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______.
विकल्प
`sqrt(3)/2`
`sqrt(2)/3`
`2/7`
`3/7`
उत्तर
The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to `2/7`.
Explanation:
Direction ratios of the normal to the plane 2x – 3y + 6z – 11 = 0 are 2, – 3, 6
Direction ratios of x-axis are 1, 0, 0
∴ Angle between plane and line is
`sin theta = (2(1) - 3(0) + 6(0))/(sqrt((2)^2 + (-3)^2 + (6^2))*sqrt((1)^2 + (0)^2 + (0)^2)`
= `2/sqrt(4 + 9 + 36)`
= `2/7`
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