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Question
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
Options
`(2x)/sqrt(3) = y/2 = z/0`
`(2x)/sqrt(3) = (2y)/1 = z/0`
2x = `(2y)/sqrt(3) = z/1`
`(2x)/sqrt(3) = (2y)/1 = z/1`
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Solution
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is `underlinebb((2x)/sqrt(3) = (2y)/1 = z/0)`.
Explanation:
Here, direction cosines of the line are
l = cos 30°, m = cos 60°, n = cos 90°
l = `sqrt(3)/2`, m = `1/2`, n = 0
Here, line passes through the point (0, 0, 0).
So, the required equation of line is
`(x - 0)/(sqrt(3)/2) = (y - 0)/(1/2) = (z - 0)/0`
`\implies (2x)/sqrt(3) = (2y)/1 = z/0`
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