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Q.

Which of the following is/are correct regarding vectors A→=i^+j^ and B→=2i^−3j^ ?

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a

Angle between A→and B→ is acute

b

Angle between A→ + B→ and A→ is acute

c

k^ is a unit vector perpendicular to A→.

d

i^−j^2is a unit vector perpendicular to A→.

answer is B.

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Detailed Solution

(a) A→⋅B→=2−3=−1⇒ angle between A→ and B→>90∘(b) (A→+B→)⋅A→=(3i^−2j^)⋅(i^+j^)=3−2=1       ⇒ Option (b) is correct (c) k^ is ⊥ to all vectors in x−y plane (d) (i^+j^)⋅i^−j^2=0Therefore it is perpendicular to A→
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Which of the following is/are correct regarding vectors A→=i^+j^ and B→=2i^−3j^ ?