(B) The points are $A(-2, 1)$ and $B(3, -4)$.Using the section formula,point $C$ divides $AB$ in the ratio $m:n = 1:2$.$C = \left( \frac{1(3) + 2(-2)}

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(B) The points are $A(-2, 1)$ and $B(3, -4)$.Using the section formula,point $C$ divides $AB$ in the ratio $m:n = 1:2$.$C = \left( \frac{1(3) + 2(-2)}{1+2}, \frac{1(-4) + 2(1)}{1+2} \right) = \left( \frac{3-4}{3}, \frac{-4+2}{3} \right) = \left( -\frac{1}{3}, -\frac{2}{3} \right)$.Since $C$ lies in the third quadrant,its argument is $\theta = \tan^{-1}\left( \frac{y}{x} \right) - \pi$.$\text{arg}(C) = \tan^{-1}\left( \frac{-2/3}{-1/3} \right) - \pi = \tan^{-1}(2) - \pi$.

Class 11 Mathematics 4-1.Complex numbers Geometry of complex numbers

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If $C$ is a point on the straight line joining the points $A(-2+i)$ and $B(3-4i)$ in the Argand plane and $\frac{AC}{CB}=\frac{1}{2}$,then the argument of $C$ is

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A
$\tan^{-1} 3$
B
$\tan^{-1} 2 - \pi$
C
$\tan^{-1} 2$
D
$\pi - \tan^{-1} 3$

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