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Analytical Geometry

Blazing goIITian

Joined:	19 Feb 2007
Post:	1802

21 Oct 2007 13:59:16 IST

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3d geometry - 2

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q) The angle between the line x=y=z and the plane 4x - 3y + 5z = 2 is....?

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Priyesh

Blazing goIITian

Joined: 18 Feb 2007

Posts: 1042

21 Oct 2007 14:17:03 IST

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angle between line & plane is 90 - (angle between line & normal vector)

now direction ratio of line is i + j + k

& D.R of normal vector is 4i -3j + 5k

therefore angle between line & normal vector can be given by dot product

therefore cos(theta) = (4 -3 + 5)/[root(3)*5root(2)] = root(6)/5 => theta is cos^-1 root(6) / 5

now angle needed is pi/2 - theta = pi/2 - cos^-1(root(6) / 5) = sin^-1(root(6) / 5)

joy francis

Blazing goIITian

Joined: 19 Feb 2007

Posts: 1802

21 Oct 2007 14:47:08 IST

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correct....good work!!

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