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