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The resultant of three vectors 1,2, and ...

The resultant of three vectors 1,2, and 3 units whose directions are those of the sides of an equilateral triangle is at what angle with respect to first vector?

A

`30^(@)` with the first vector

B

`15^(@)` with the first vector

C

`100^(@)` with the first vector

D

`150^(@)` with the first vector

Text Solution

Verified by Experts

The correct Answer is:
D
Analytically,
`R_(x) =1 +2 cos 120^(@) +3 sin 240^(@)`
`= 2 xx(sqrt(3))/(2) +3xx(-sqrt(3)/(2))=-(sqrt(3))/(2)`
`tan theta=(R_(y))/(R_(x))=((-sqrt(3))/(2))/(-(3)/(2))=(sqrt(3))/(3)=(1)/(sqrt(3))implies theta=30^(@)`
Hence angle with first vector is `80^(@)-theta=150^(@)`
Graphically AB =1 BC =2, CD=3
`vecR= vec(AD)` is resultant clearly angle between `vecR` and `vec(AB)` is `150^(@)` .
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