Two forces each numerically equal to 25N are acting as shown in the following figure. What is the resultant vector?
A
|→R|=25N at an angle of 60∘ clockwise from →A
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B
|→R|=25N at an angle of 120∘ clockwise from →A
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C
|→R|=25N at an angle of 30∘ clockwise from →A
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D
|→R|=30N at an angle of 75∘ clockwise from →A
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Solution
The correct option is A|→R|=25N at an angle of 60∘ clockwise from →A Given, vector →A and →B, each has |→A|=|→B|=25N and from the figure it can be seen that angle between →A and →B is 120∘ resultanatn vector →R, →R=→A+→B |→R|=√|→A|2+|→B|2+2×|→A|×|→B|×cosθ |→R|=√252+252+2×25×25×cos(120∘) |→R|=√252+252+2×25×25×(−12) |→R|=√252 |→R|=25N And, tanα=25×sin120∘25+25×cos120∘