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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» <html><body><p></p>Solution :(a) Incorrect , if is not necessary that `vec a, vecb , vecc` and `vecd` each should be a null <a href="https://interviewquestions.tuteehub.com/tag/vector-20923" style="font-weight:bold;" target="_blank" title="Click to know more about VECTOR">VECTOR</a> . `vec a +vec b+vec <a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a> +vec d ` can be <a href="https://interviewquestions.tuteehub.com/tag/zero-751093" style="font-weight:bold;" target="_blank" title="Click to know more about ZERO">ZERO</a> by amny other ways . <br/> (b)Correct, `vec a+vec b+vec c +vec d =vec0` <br/> The `vec a+vecc=-(vecb+vecd)` <br/> `|vec a +vec c|=|vecb+vecd|` <br/> (c) Correct , `veca +vec b+vec c +vec d =0` <br/> `vec a=-(vec b+vec c +vec d)` <br/> Magnitude of `veca` can never be grater than <br/> `(vec b+vec c+vec d)`<br/> (d) `vec a+vec b+vec C+vec d=vec 0` <br/> We can write `veca+ (vec b+vec c )+vec d=0` <br/> Now `(vec a +vec b+vec c+vec d)` is zero only if`( vec b +vec c )` must <a href="https://interviewquestions.tuteehub.com/tag/lie-1073081" style="font-weight:bold;" target="_blank" title="Click to know more about LIE">LIE</a> in the plane of `veca and vecd` <br/> 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 .</body></html>


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