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).

∵R=a+b ∴ b=R-a ⇒ b2=R2+a2-2Racos30° ⇒ b2=4+12-2×2×23×32 ⇒ b2=16-12=4 ∴ b=2 N

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).

∵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 $2 \sqrt{3} N$ and makes an angle of $30 °$ with the resultant. Find the magnitude of $b$ (in newton).

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16 N

6 N

12 N

2 N

answer is C.

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$∵ R = a + b ∴ b = R - a \Rightarrow b^{2} = R^{2} + a^{2} - 2 Racos 30 ° \Rightarrow b^{2} = 4 + 12 - 2 \times 2 \times 2 \sqrt{3} \times \frac{\sqrt{3}}{2} \Rightarrow b^{2} = 16 - 12 = 4 ∴ b = 2 N$

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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).

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The resultant of two vectors a and b has magnitude $2 N$ . The magnitude of $a$ is $2 \sqrt{3} N$ and makes an angle of $30 °$ with the resultant. Find the magnitude of $b$ (in newton).