Two vectors having equal magnitude A and making an angle theta with each other. What will be the magnitude and direction of the resultant?
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Two vectors having equal magnitude A and making an angle theta with each other. What will be the magnitude and direction of the resultant?
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Answer:
R=2Csin∆/2
tan @=cot ∆/2
Explanation:
hey mate
we know
R²=A²+B²+2|A||B| cos ∆
If A=B=C,
then
=>R²=2C²+2C²cos ∆
=>R²=2C²(1+cos ∆)
=>R²=2C²*2 sin²∆/2 [1+cos²∆=2sin²∆/2]
=>R=2Csin ∆/2
where ∆ is angle between the two equal vectors....
tan @=|B| sin ∆/(A+ |B| cos ∆)
where @ is the angle made by resultant vector with A vector...
if A=B=C,
then,
tan @=|C| sin ∆/(|C| +|C| cos ∆)
=>tan @=sin ∆/(1+cos ∆)
=>tan @=sin ∆/(2 sin²∆/2)
=>tan @=(2sin ∆/2 cos ∆/2)/(2sin²∆/2)
[as sin 2∆=2 sin ∆ cos ∆]
=>tan @=cot ∆/2