If the points with position vectors 60 hat{i} | vedclass

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(A) Let the points be $A(60, 3)$, $B(40, -8)$, and $C(a, -52)$.Since the points are collinear, the area of the triangle formed by them is zero, or the

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$-40$

Vedclass · Answer

(A) Let the points be $A(60, 3)$, $B(40, -8)$, and $C(a, -52)$.Since the points are collinear, the area of the triangle formed by them is zero, or the slope of $AB$ must be equal to the slope of $BC$.Slope of $AB = \frac{-8-3}{40-60} = \frac{-11}{-20} = \frac{11}{20}$.Slope of $BC = \frac{-52-(-8)}{a-40} = \frac{-44}{a-40}$.Equating the slopes: $\frac{11}{20} = \frac{-44}{a-40}$.$11(a-40) = 20(-44)$.$11a - 440 = -880$.$11a = -440$.$a = -40$.

If the points with position vectors $60 \hat{i}+3 \hat{j}$, $40 \hat{i}-8 \hat{j}$, and $a \hat{i}-52 \hat{j}$ are collinear, then $a$ is equal to

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