1.

Given vecA + vecB + vecC + vecD = vec0, which of the following statements is not correct ?

Answer»

`vecA, vecB, vecC and vecD`must each be a null vector.
The magnitude of `(vecA + vecC)` equals the magnitude of `(vecB + vecD)`.
The magnitude of `vecA` can never be greater than the sum of the magnitudes of `vecB, vecC and vecD.`
`vecB + vecC` must lie in the plane of `vecA and vecD` if `vecA and vecD` are not collinear and in the line of `vecA and vecD`, if they are collinear.

Solution :The STATEMENT is not CORRECT. It is because `vecA + vecB + vecC + vecD`can be zero in many ways other than `vecA, vecB, vecC and vecD` being each a rull vector.
(b) The statement is correct as proved below
`vecA + vecB + vecC + vecD = vec0 or vecA + vecC = - (vecB + vecD)`
`therefore |vecA + vecC| = |vecB + vecD|`
(c ) The statement is correct and can be proved using triangular INEQUALITY.
`|vecB| + |vecC| ge|vecR|""...(i)`
`|vecR| + |vecD| ge|vecA|""...(II)`
Using (i) and (ii), `|vecA| le |vecB| + |vecC| + |vecD|`
(d) THe statement is correct as proved below
`vecA + vecB + vecC + vecD = vec0 or vecA + (vecB + vecC) + vecD = vec0`
The resultant sum of three vectors `vecA, (vecB+vecC)` and `vecD` can be zero only if `(vecB + vecC)` lies in the plane of `vecA and vecD` and these three vectors are represented by the three SIDES of a triangle taken in one order. IF `vecA and vecD` are collinear, then`(vecB + vecC)` must be in the line of `vecA and vecD`, only then the vector sum of all the vectors will be zero.


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