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Given a + b + c + d = 0, which of the following statements are not correct.
- 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?
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Verified Answer
Givena+b+c+d=0, which of the following statementsare not correct.a)a,b...
(a) Incorrect, because a + b + c + d can zero in many ways other than that (vector a, b, c, and d) must each be a null vector.
(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -(vector b + d).
Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.
(c) correct, Since (vector a + b + c + d = 0'
(vector a = -(b + c + d))
Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be greater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.
(d) Correct, because (vector a + b + c + d = 0;) hence ((vector b + c) + a + d = 0)
The resultant sum of three (vectors b + c, + a + d) can be zero only if (vector b + c) is in the plane of (vector a and d). In case vector a and d are collinear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.
(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -(vector b + d).
Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.
(c) correct, Since (vector a + b + c + d = 0'
(vector a = -(b + c + d))
Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be greater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.
(d) Correct, because (vector a + b + c + d = 0;) hence ((vector b + c) + a + d = 0)
The resultant sum of three (vectors b + c, + a + d) can be zero only if (vector b + c) is in the plane of (vector a and d). In case vector a and d are collinear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.
Most Upvoted Answer
Givena+b+c+d=0, which of the following statementsare not correct.a)a,b...
Given a, b, c, d = 0, we need to determine which of the following statements are correct.
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 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.
Let's analyze each statement one by one.
a) a, b, c, d must each be a null vector.
Since a, b, c, and d are all equal to 0, they are indeed null vectors. Therefore, statement a is correct.
b) The magnitude of (a + c) equals the magnitude of (b + d).
Since a, b, c, and d are all null vectors, their sum (a + c) and (b + d) will also be null vectors. The magnitude of a null vector is always 0. Therefore, statement b is correct.
c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.
Since a, b, c, and d are all null vectors, their magnitudes are all 0. The sum of the magnitudes of b, c, and d is also 0. Therefore, the magnitude of a can never be greater than 0. Hence, statement c is correct.
d) b 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.
Since a and d are both null vectors, they do not define a line or a plane. Therefore, it is not possible to determine whether b lies in the plane of a and d or in the line of a and d based on the given information. Hence, statement d is incorrect.
In conclusion, the correct statements are a, b, and c.
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 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.
Let's analyze each statement one by one.
a) a, b, c, d must each be a null vector.
Since a, b, c, and d are all equal to 0, they are indeed null vectors. Therefore, statement a is correct.
b) The magnitude of (a + c) equals the magnitude of (b + d).
Since a, b, c, and d are all null vectors, their sum (a + c) and (b + d) will also be null vectors. The magnitude of a null vector is always 0. Therefore, statement b is correct.
c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d.
Since a, b, c, and d are all null vectors, their magnitudes are all 0. The sum of the magnitudes of b, c, and d is also 0. Therefore, the magnitude of a can never be greater than 0. Hence, statement c is correct.
d) b 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.
Since a and d are both null vectors, they do not define a line or a plane. Therefore, it is not possible to determine whether b lies in the plane of a and d or in the line of a and d based on the given information. Hence, statement d is incorrect.
In conclusion, the correct statements are a, b, and c.
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Community Answer
Givena+b+c+d=0, which of the following statementsare not correct.a)a,b...
(a) Incorrect, because a + b + c + d can zero in many ways other than that (vector a, b, c, and d) must each be a null vector.
(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -(vector b + d).
Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.
(c) correct, Since (vector a + b + c + d = 0'
(vector a = -(b + c + d))
Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be greater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.
(d) Correct, because (vector a + b + c + d = 0;) hence ((vector b + c) + a + d = 0)
The resultant sum of three (vectors b + c, + a + d) can be zero only if (vector b + c) is in the plane of (vector a and d). In case vector a and d are collinear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.
(b) Correct, as (vector a + b + c + d = 0;) (vector a + c) = -(vector b + d).
Thus, (vector a + b) is equal to negative of( vector b + d) and hence the statement that magnitude of (vector A + C) is equal to the magnitude of (vector b + d) is correct.
(c) correct, Since (vector a + b + c + d = 0'
(vector a = -(b + c + d))
Thus, magnitude of vector a is equal to (vector b + c + d). The sum of the magnitude of (vectors b + c) and d may be greater than or equal to that of vector a. Hence the statement that the magnitude of vector a can never be greater than the sum of the magnitude of (vector b, c and d) is correct.
(d) Correct, because (vector a + b + c + d = 0;) hence ((vector b + c) + a + d = 0)
The resultant sum of three (vectors b + c, + a + d) can be zero only if (vector b + c) is in the plane of (vector a and d). In case vector a and d are collinear, (vector b + c) must be the line of (vector a and d.) Hence the given statement is correct.
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Givena+b+c+d=0, which of the following statementsare not correct.a)a,b,c,dmust each be a null vector,b)The magnitude of (a + c)equals the magnitude of(b+d),c)The magnitude ofacan never be greater than thesum of the magnitudes ofb,candd,d)b+cmust lie in the plane ofaanddifaanddarenot collinear, and in the line ofaandd, if theyarecollinear?Correct answer is option 'A'. Can you explain this answer?
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Givena+b+c+d=0, which of the following statementsare not correct.a)a,b,c,dmust each be a null vector,b)The magnitude of (a + c)equals the magnitude of(b+d),c)The magnitude ofacan never be greater than thesum of the magnitudes ofb,candd,d)b+cmust lie in the plane ofaanddifaanddarenot collinear, and in the line ofaandd, if theyarecollinear?Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Givena+b+c+d=0, which of the following statementsare not correct.a)a,b,c,dmust each be a null vector,b)The magnitude of (a + c)equals the magnitude of(b+d),c)The magnitude ofacan never be greater than thesum of the magnitudes ofb,candd,d)b+cmust lie in the plane ofaanddifaanddarenot collinear, and in the line ofaandd, if theyarecollinear?Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Givena+b+c+d=0, which of the following statementsare not correct.a)a,b,c,dmust each be a null vector,b)The magnitude of (a + c)equals the magnitude of(b+d),c)The magnitude ofacan never be greater than thesum of the magnitudes ofb,candd,d)b+cmust lie in the plane ofaanddifaanddarenot collinear, and in the line ofaandd, if theyarecollinear?Correct answer is option 'A'. Can you explain this answer?.
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