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What is the value of n so that the angle between the lines having direction ratios (1, 1, 1) and (1, –1, n) is 60°?
- a)√3
- b)√6
- c)3
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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What is the value of n so that the angle between the lines having dire...
If (l1, m1, n1) and (l2, m2, n2) are the direction ratios then angle between the lines is
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What is the value of n so that the angle between the lines having dire...
The angle between two lines with direction ratios (a, b, c) and (d, e, f) can be found using the formula:
cosθ = (ad + be + cf) / √(a² + b² + c²) * √(d² + e² + f²)
In this case, we have (1, 1, 1) and (1, n, n). Plugging these values into the formula, we get:
cosθ = (1*1 + 1*n + 1*n) / √(1² + 1² + 1²) * √(1² + n² + n²)
= (1 + 2n) / √(3) * √(1 + 2n²)
To find the value of n, we need to find the value of cosθ. Let's say the angle between the lines is θ. If we take the cosine inverse of both sides, we get:
θ = cos^(-1)((1 + 2n) / √(3) * √(1 + 2n²))
Since the angle between two lines cannot be negative, we can ignore the negative sign on the right side. Therefore, we have:
θ = cos^(-1)((1 + 2n) / √(3) * √(1 + 2n²)) >= 0
Now, we need to find the value of n that satisfies this inequality.
cosθ = (ad + be + cf) / √(a² + b² + c²) * √(d² + e² + f²)
In this case, we have (1, 1, 1) and (1, n, n). Plugging these values into the formula, we get:
cosθ = (1*1 + 1*n + 1*n) / √(1² + 1² + 1²) * √(1² + n² + n²)
= (1 + 2n) / √(3) * √(1 + 2n²)
To find the value of n, we need to find the value of cosθ. Let's say the angle between the lines is θ. If we take the cosine inverse of both sides, we get:
θ = cos^(-1)((1 + 2n) / √(3) * √(1 + 2n²))
Since the angle between two lines cannot be negative, we can ignore the negative sign on the right side. Therefore, we have:
θ = cos^(-1)((1 + 2n) / √(3) * √(1 + 2n²)) >= 0
Now, we need to find the value of n that satisfies this inequality.
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What is the value of n so that the angle between the lines having direction ratios (1, 1, 1) and (1, –1, n) is 60°?a)√3b)√6c)3d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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