Question

Two vectors having equal magnitude A and making an angle theta with each other. What will be the magnitude and direction of the resultant?

Answer 1

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