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Question
The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______.
Options
`sqrt(3)/2`
`sqrt(2)/3`
`2/7`
`3/7`
Solution
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:
Equation of plane is 2x – 3y + 6z – 11 = 0
or `vecn = 2hati - 3hatj + 6hatk`
Equation of line is `vecb = hati`
`sin theta = (vecb * vecn)/(|vecb||vecn|)`
`sin(sin^-1alpha) = ((2hati - 3hatj + 6hatk)*(hati + 0hatj + 0hatk))/(sqrt((2)^2 + (-3)^2 + (6)^2 * ssqrt((1)^2)`
`alpha = 2/sqrt(49)`
`alpha = 2/7`
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