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Question
If the directions cosines of a line are k, k, k, then ______.
Options
k > 0
0 < k < 1
k = 1
k = `1/sqrt(3)` or `- 1/sqrt(3)`
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Solution
If the directions cosines of a line are k, k, k, then k = `1/sqrt(3)` or `- 1/sqrt(3)`.
Explanation:
If l, m, n are the direction cosines of a line, then
l2 + m2 + n2 = 1
So, k2 + k2 + k2 = 1
⇒ 3k2 = 1
⇒ l = `+- 1/sqrt(3)`
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