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Question

Vector A having magnitude 2 units makes an angle 45 with horizontal and vector B having magnitude 2 units makes an angle 30 with horizontal as shown in the figure. What is AB?


A
(1+3)^i+2^j
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B
(1+3)^i2^j
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C
(13)^i+2^j
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D
(13)^i
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Solution

The correct option is D (13)^i
Taking components along the axes, the vector A can be written as
A=(2cos45)^i+(2sin45)^j
=^i+^j
The vector B can be written as
B=(2cos30)^i+(2sin30)^j
=3^i+^j

Hence,
A B
=(^i+^j)(3^i+^j)
=(13)^i

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