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The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______. - Mathematics

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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`

MCQ
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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:

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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अध्याय 12: Introduction to Three Dimensional Geometry - Exercise [पृष्ठ २३८]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 12 Introduction to Three Dimensional Geometry
Exercise | Q 36 | पृष्ठ २३८

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