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Question -

If a line makes angles 90┬░, 135┬░, 45┬░ with the x, y and z-axes respectively, find its direction cosines.



Answer -

Let the direction cosines of the line be l, m and n.
Here let ╬▒ = 90┬░, ╬▓ = 135┬░ and ╬│ = 45┬░
So,
l = cos ╬▒, m = cos ╬▓ and n = cos ╬│
So direction cosines are
l = cos 90┬░ = 0
m = cos 135┬░= cos (180┬░ тАУ 45┬░) = -cos 45┬░ = -1/тИЪ2
n = cos 45┬░ = 1/тИЪ2
тИ┤ The direction cosines of the line are 0, -1/тИЪ2, 1/тИЪ2

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