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Question

# Vector →A of magnitude 4 units is directed along the positive x-axis. Another vector →B of magnitude 3 units lies in the x-y plane and makes an angle 30∘ with the positive x-axis as shown in the figure. Then →A.→B is

A

6 units

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B

62 units

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C

63 units

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D

12 units

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Solution

## The correct option is C 6√3 units Let ^i and ^j be the unit vectors along positive x and y axes respectively. Then →A=4^i →B=3 cos 30∘^i+3 sin 30∘^j =3√32^i+32^j →A.→B=4^i.(3√32^i+32^j)=6√3 (∵^i.^i=1;^i.^j=0). Hence, the correct option is (c).

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