The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B, The angle between A and B is

Question

Infinity Learn · Accepted Answer

Here (A+B)⋅$$A=0A2+ABcos$$⁡θ$$=0or$$ ABcos⁡θ$$=$$−$$A2$$....(1)Bcos$$⁡θ$$=$$−A...$$(2)Further$$, |$$A+B$$|$$=12$$|B|or $$(A+B)⋅(A+B)=12$$|B|$$2A2+B2+2ABcos$$⁡θ$$=14B2or$$ $$A2+ABcos$$⁡θ$$+B2+ABcos$$⁡θ$$=14B20+B2+ABcos$$⁡θ$$=$$−$$14B2or$$ ABcos⁡θ$$=$$−$$34B2$$ …$$(3)From$$ eqs. $$(1) and (3)A2=34B2$$ or $$A=(3/2)BFrom$$ eq. $$(2), Bcos⁡θ$$=$$−$$(3/2)Bor$$ $$cos$$⁡θ$$=$$−$$3/2$$ or θ$$=150$$∘

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B, The angle between A and B is

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