It is found that |A+B|=|A|. This necessarily implies,

(a) B = 0

(b) A,B are antiparallel

(c) A,B are perpendicular

(d) A.B ≤ 0

<p>This is a Multiple Choice Questions as classified in NCERT Exemplar</p><p><strong>Answer- b, d</strong></p><p><strong>Explanation</strong> – given A+B+C = 0</p><p>B<span contenteditable="false"> <math> <mo>×</mo> <mfenced separators="|"> <mrow> <mrow> <mi>A</mi> <mo>+</mo> <mi>B</mi> <mo>+</mo> <mi>C</mi> </mrow> </mrow> </mfenced> <mo>=</mo> <mi>B</mi> <mo>×</mo> <mn>0</mn> <mo>=</mo> <mn>0</mn> </math> </span></p><p>B<span contenteditable="false"> <math> <mo>×</mo> <mi>A</mi> </math> </span>+B<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> <mo>+</mo> <mi>B</mi> <mo>×</mo> <mi>C</mi> </math> </span>=0</p><p>B<span contenteditable="false"> <math> <mo>×</mo> <mi>A</mi> <mo>+</mo> <mn>0</mn> <mo>+</mo> <mi>B</mi> <mo>×</mo> <mi>C</mi> <mo>=</mo> <mn>0</mn> </math> </span></p><p>B<span contenteditable="false"> <math> <mo>×</mo> <mi>A</mi> <mo>=</mo> <mo>-</mo> <mi>B</mi> <mo>×</mo> <mi>C</mi> </math> </span></p><p>A<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> <mo>=</mo> <mi>B</mi> <mo>×</mo> <mi>C</mi> </math> </span></p><p> (A<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> </math> </span>)<span contenteditable="false"> <math> <mo>×</mo> <mi>C</mi> <mo>=</mo> <mfenced separators="|"> <mrow> <mrow> <mi>B</mi> <mo>×</mo> <mi>C</mi> </mrow> </mrow> </mfenced> <mo>×</mo> <mi>C</mi> </math> </span></p><p>It cannot be zero</p><p> (b) (A<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> </math> </span>).C= (B<span contenteditable="false"> <math> <mo>×</mo> <mi>A</mi> <mi>C</mi> </math> </span>).C=0 . if b|C then B<span contenteditable="false"> <math> <mo>×</mo> <mi>C</mi> </math> </span>=0 then (B<span contenteditable="false"> <math> <mo>×</mo> <mi>C</mi> </math> </span>)<span contenteditable="false"> <math> <mo>×</mo> <mi>C</mi> <mo>=</mo> <mn>0</mn> </math> </span></p><p> (c) (A<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> </math> </span>)=X=ABsin<span contenteditable="false"> <math> <mi>θ</mi> <mi> </mi> <mi>X</mi> </math> </span>. The direction of X is perpendicular to the plane containing A and B (A<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> </math> </span>)<span contenteditable="false"> <math> <mo>×</mo> <mi>C</mi> <mo>=</mo> <mi>X</mi> <mo>×</mo> <mi>C</mi> <mo>.</mo> <mi> </mi> </math> </span></p><p> (d) if c²= A²+B², then angle between A and B is 90⁰</p><p> (A<span contenteditable="false"> <math> <mo>×</mo> <mi>B</mi> </math> </span>).C= (AB sin90⁰X).C=AB (X.C)</p><p>= ABC cos90⁰= 0</p>

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