NEET Exam > NEET Questions > Given a + b + c + d = 0, which of the followi...
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Given a + b + c + d = 0, which of the following statements is incorrect?
- a)a, b, c, d must each be a null vector.
- b)The magnitude of (a + c) equals the magnitude of (b + d).
- c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.
- d)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.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Given a + b + c + d = 0, which of the following statements is incorrec...
(a) Incorrect, because a + b + c + d can be zero in many ways other than each of a, b, c, and d being a null vector.
(b) Correct, as a + b + c + d = 0 implies a + c = -(b + d). Thus, the magnitude of (a + c) is equal to the magnitude of (b + d).
(c) Correct, since a + b + c + d = 0, so a = -(b + c + d). The magnitude of a is equal to the magnitude of (b + c + d). The sum of the magnitudes of b, c, and d will always be greater than or equal to the magnitude of a, so the statement is correct.
(d) Correct, because a + b + c + d = 0 means (b + c) + (a + d) = 0. The resultant sum of three vectors (b + c), a, and d can be zero only if (b + c) is in the plane of a and d. If a and d are collinear, then (b + c) must be along the line of a and d. Hence, the statement is correct.
(b) Correct, as a + b + c + d = 0 implies a + c = -(b + d). Thus, the magnitude of (a + c) is equal to the magnitude of (b + d).
(c) Correct, since a + b + c + d = 0, so a = -(b + c + d). The magnitude of a is equal to the magnitude of (b + c + d). The sum of the magnitudes of b, c, and d will always be greater than or equal to the magnitude of a, so the statement is correct.
(d) Correct, because a + b + c + d = 0 means (b + c) + (a + d) = 0. The resultant sum of three vectors (b + c), a, and d can be zero only if (b + c) is in the plane of a and d. If a and d are collinear, then (b + c) must be along the line of a and d. Hence, the statement is correct.
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Given a + b + c + d = 0, which of the following statements is incorrec...
Understanding the Statement
The equation a + b + c + d = 0 implies a balance among the vectors a, b, c, and d. This means that the vector sum of these four vectors results in a null vector.
Analysis of Each Option
a) a, b, c, d must each be a null vector.
- Incorrect Statement: This is not true because the vectors do not need to be null vectors individually. They can have non-zero magnitudes but still satisfy the equation if they balance each other out. For example, if a = 1, b = -1, c = 1, and d = -1, the sum is zero, but none of them are null vectors.
b) The magnitude of (a + c) equals the magnitude of (b + d).
- True Statement: Since a + b + c + d = 0 can be rearranged to a + c = - (b + d), the magnitudes of (a + c) and (b + d) will be equal.
c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.
- True Statement: This is consistent with the triangle inequality in vector addition, ensuring that no single vector can exceed the combined effect of the others.
d) 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.
- True Statement: This follows from the geometric properties of vectors, maintaining the balance in the vector equation.
Conclusion
The correct answer is option 'A' because a, b, c, and d do not need to be null vectors individually to satisfy a + b + c + d = 0.
The equation a + b + c + d = 0 implies a balance among the vectors a, b, c, and d. This means that the vector sum of these four vectors results in a null vector.
Analysis of Each Option
a) a, b, c, d must each be a null vector.
- Incorrect Statement: This is not true because the vectors do not need to be null vectors individually. They can have non-zero magnitudes but still satisfy the equation if they balance each other out. For example, if a = 1, b = -1, c = 1, and d = -1, the sum is zero, but none of them are null vectors.
b) The magnitude of (a + c) equals the magnitude of (b + d).
- True Statement: Since a + b + c + d = 0 can be rearranged to a + c = - (b + d), the magnitudes of (a + c) and (b + d) will be equal.
c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.
- True Statement: This is consistent with the triangle inequality in vector addition, ensuring that no single vector can exceed the combined effect of the others.
d) 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.
- True Statement: This follows from the geometric properties of vectors, maintaining the balance in the vector equation.
Conclusion
The correct answer is option 'A' because a, b, c, and d do not need to be null vectors individually to satisfy a + b + c + d = 0.
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Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer?.
Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Given a + b + c + d = 0, which of the following statements is incorrect?a)a, b, c, d must each be a null vector.b)The magnitude of (a + c) equals the magnitude of (b + d).c)The magnitude of a can never be greater than the sum of the magnitudes of b, c and d.d)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.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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