Question

4.
The resultant of two vectors at an angle 150° is 10
units and is perpendicular to one vector. The
magnitude of the smaller vector is
(1) 10 units
(2) 10/3 units
(3) 10v3 units
(4) 5v3 units

Answer 1

Answer:

The resultant of two vectors at an angle 150 is 10 units and is perpendicular to one vector. The magnitude of the smaller vector is (1) 10 units (3) 10 sqrt2 units

Answer 2

Answer:

Explanation:

Since,

tanβ=AsinΘ/A+BcosΘ

Where β is the angle b/w the resultant & one vector

So, tan90°=Asin150°/A+Bcos150°

∞=A/2/A+B(-√3/2)

=>2A-√3B=0

2A=√3B

=>4A^2=3B^2.

A^2=3B^2/4

Since,R=√A2+B2+2ABcosΘ

100=A2+B2+2ABcos150°

100=3B^2/4+B^2+2B(√3B×√3)/4

=>> B=20/3=6.66----

So, A=√3(20/3)/2=10/√3=5.77

So, magnitude of smaller vector is 5.77

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