Three vectors act at a point ‘O’ as shown in figure . For given value of P and $θ$ the correct options are

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for value P = 10N , $θ = 30 °$ the resultant is a null vector

The resultant is a null vector if $θ = 0$ , $\bar{P} = 10 \sqrt{2} N$

The resultant is $(30 i) N$ , if $θ = \frac{3 π}{2} P = 10 N$ in magnitude

The resultant is 10N if $θ = 90 °$ , , $\bar{P} = 10 N$

answer is B, C.

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Detailed Solution

a) If $θ = 0$ and $P = 10 \sqrt{2} N$ then resultant is $= \sqrt{P^{2} + 20^{2}} = \sqrt{200 + 400} = 10 \sqrt{6} N$

b) If $θ = 90 °$ and P = 10Nthe resultant = 10N

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If $θ = \frac{3 π}{2}$ and P = 10N; The resultant is $= 30 \hat{i}$
d)

If P = 10 N and $θ = 30 °$ ; Resultant $\vec{R} = 15 \hat{i} + 5 \sqrt{3} \hat{j}$

$R = \sqrt{225 + 75} = \sqrt{300} = 10 \sqrt{3} N$

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