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Give ` vec A + vec B+ vec C + vec D` =0`, which of the following statements are correct ? (a) ` vec A, vec B ,vec C ` abd ` vec C` must each be a null vector. (b) The magnitude of ` ( vec A + vec C)` equals the magnitude of ` ( vec B + vec D0`. ltBrgt (c ) The magnitude of ` vec A` can never be greater than the sum of the magnitude of ` vec B , vec C ` and vec D`. ( d) ` vec B + vec C` must lie in the plance of ` vec A + vec D. if vec A and vec D` are not colliner and in the line of ` vec A` and `vec D`, if they are collinear. |
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Answer» (a) Not correct, because ` vec A + vec B+ vec C+ vec D` can be zero in may ways other than ` vec A, vec B, vec C` and ` vwc D` must each be a null vector. ltBrgt ( b) Correct. Since, ` vec A+ vec B+ vec C+ vec D=0 , (c ) Correct. Since ` vec A + vec B+ vec C + vec D=0` or ` vec A =- ( vec B+ vec C+ vec D)` It means the magnitude of ` vec A` is equal to the maniude of vector (vec B+ vec C + vec D). Since the sum of the magnitudes of ` vec B, vec C` and vec D` may be equal or greater than the magnitude of ` vec A`, hence the magnitude of `vec A` can never be greate than the sum of the maniude of ` vec B, vec C ` and vec D`. (d) Correct, Since ` vec A + vec B= vec D =0 , or vec A = 9 vec B= vec C) + vec D=0` and these three vectors are represented by the three sides of a triangle taken in one order. If ` vec A ` and ` vec B` are collinear, the ( vec B +vec C) must be in line of ` vec A` and vec D` , only then the vector sum of all the vectors will be zero. |
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