triangle ABC has vertices at A equiv (2, 3, 5 | vedclass

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(D) Let $D$ be the midpoint of $BC$. The coordinates of $D$ are given by: $D = \left( \frac{\lambda - 1}{2}, \frac{5 + 3}{2}, \frac{\mu + 2}{2} \right

Vedclass · Accepted Answer

$7, 10$

Vedclass · Answer

(D) Let $D$ be the midpoint of $BC$. The coordinates of $D$ are given by: $D = \left( \frac{\lambda - 1}{2}, \frac{5 + 3}{2}, \frac{\mu + 2}{2} \right) = \left( \frac{\lambda - 1}{2}, 4, \frac{\mu + 2}{2} \right)$. The direction ratios of the median $AD$ are given by the difference of the coordinates of $D$ and $A$: $AD = \left( \frac{\lambda - 1}{2} - 2, 4 - 3, \frac{\mu + 2}{2} - 5 \right) = \left( \frac{\lambda - 5}{2}, 1, \frac{\mu - 8}{2} \right)$. Since the median $AD$ is equally inclined to the coordinate axes,its direction ratios must be proportional to $(1, 1, 1)$ or $(\pm 1, \pm 1, \pm 1)$. Thus,we have: $\frac{\lambda - 5}{2} = 1 \implies \lambda - 5 = 2 \implies \lambda = 7$. $\frac{\mu - 8}{2} = 1 \implies \mu - 8 = 2 \implies \mu = 10$. Therefore,the values are $\lambda = 7$ and $\mu = 10$.

$\triangle ABC$ has vertices at $A \equiv (2, 3, 5)$,$B \equiv (-1, 3, 2)$ and $C \equiv (\lambda, 5, \mu)$. If the median through $A$ is equally inclined to the axes,then the values of $\lambda$ and $\mu$ respectively are

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