Given a+b+cd+c=0 , which of the following statements are correct? (a) veca, vecb, vecc and vecd must each be a null vector . (b) The magnitude of (veca+vecc) equals the magnitude of (b+d) (c) The magnitude of veca can never be greater than the sum of the magnitudes of vecb, vecc and vecc. (d) vecb+vecc must lie in the plane of vec a and vecd if veca and vecd are not collinear ,and in the line of vec a and vec d, if they are collinear.

Given a+b+cd+c=0 , which of the following statements are correct? (a)

1.	Given a+b+cd+c=0 , which of the following statements are correct? (a) veca, vecb, vecc and vecd must each be a null vector . (b) The magnitude of (veca+vecc) equals the magnitude of (b+d) (c) The magnitude of veca can never be greater than the sum of the magnitudes of vecb, vecc and vecc. (d) vecb+vecc must lie in the plane of vec a and vecd if veca and vecd are not collinear ,and in the line of vec a and vec d, if they are collinear.
Answer» Solution :(a) Incorrect , if is not necessary that `vec a, vecb , vecc` and `vecd` each should be a null VECTOR . `vec a +vec b+vec C +vec d ` can be ZERO by amny other ways . (b)Correct, `vec a+vec b+vec c +vec d =vec0` The `vec a+vecc=-(vecb+vecd)` `\|vec a +vec c\|=\|vecb+vecd\|` (c) Correct , `veca +vec b+vec c +vec d =0` `vec a=-(vec b+vec c +vec d)` Magnitude of `veca` can never be grater than `(vec b+vec c+vec d)` (d) `vec a+vec b+vec C+vec d=vec 0` We can write `veca+ (vec b+vec c )+vec d=0` Now `(vec a +vec b+vec c+vec d)` is zero only if`( vec b +vec c )` must LIE in the plane of `veca and vecd` But if `vec a and vec d` are collinear, then `(vec b +vec c)` must lie in theline of `vec a and vec d`, only then the vectorsumofall thevectors will be zero .