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प्रश्न
Given a + b + c + d = 0, state whether the following statement is correct or incorrect:
b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear.
विकल्प
Correct
Incorrect
उत्तर
This statement is Correct.
Explanation:
∴ a + b + c + d = 0
∴ a + c = (b + d)
∴ b + d = (a + c)
If a + d are not collinear, then a + d will be in the plane of a and d.
Therefore, b + d = -(a + d) will also be in the plane of a + d. If a and d are collinear, then -(a + d) will also be collinear with a and d; therefore, b + c will also be parallel to a and d.
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संबंधित प्रश्न
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- | a+b | ≤ |a| + |b|
- |a + b| ≥ | |a| - |b| |
- |a - b| ≤ |a| + |b|
- |a-b| ≥ | |a| - |b| |
When does the equality sign above apply?
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The magnitude of (a + c) equals the magnitude of (b + d).
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| Column I | Column II | ||
| (a) | a + b = c | (i) |  |
| (b) | a – c = b | (ii) |  |
| (c) | b – a = c | (iii) |  |
| (d) | a + b + c = 0 | (iv) |  |
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