Q.

The resultant of two vectors a and b has magnitude 2 N. The magnitude of a is 23 N and makes an angle of 30° with the resultant. Find the magnitude of b (in newton).

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a

12 N

b

16 N

c

2 N

d

6 N

answer is C.

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Detailed Solution

∵R=a+b ∴  b=R-a ⇒  b2=R2+a2-2Racos30° ⇒  b2=4+12-2×2×23×32 ⇒  b2=16-12=4 ∴  b=2 N
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The resultant of two vectors a and b has magnitude 2 N. The magnitude of a is 23 N and makes an angle of 30° with the resultant. Find the magnitude of b (in newton).