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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 A+B?


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

The correct option is A (1 + 3) ^i + 2 ^j
Taking components the vector A can be written as
A = (2 cos (45) ^i + 2 sin (45) ^j )
= ^i + ^j
Taking components the vector B can be written as
B = (2 cos (30 ) ^i + 2 sin (30) ^j )
= 3 ^i + ^j

Hence,
A + B
= (^i + ^j) + (3 ^i + ^j)
= (1 + 3) ^i + 2 ^j

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