If the points (-1, -1, 2), (2, m, 5) and (3, | vedclass

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(A) Let the given points be $A(-1, -1, 2), B(2, m, 5)$ and $C(3, 11, 6)$.Since the points are collinear,the vectors $\overrightarrow{AB}$ and $\overri

Vedclass · Accepted Answer

$m = 8$

Vedclass · Answer

(A) Let the given points be $A(-1, -1, 2), B(2, m, 5)$ and $C(3, 11, 6)$.Since the points are collinear,the vectors $\overrightarrow{AB}$ and $\overrightarrow{BC}$ must be parallel.$\overrightarrow{AB} = (2 - (-1))\hat{i} + (m - (-1))\hat{j} + (5 - 2)\hat{k} = 3\hat{i} + (m + 1)\hat{j} + 3\hat{k}$.$\overrightarrow{BC} = (3 - 2)\hat{i} + (11 - m)\hat{j} + (6 - 5)\hat{k} = 1\hat{i} + (11 - m)\hat{j} + 1\hat{k}$.Since $\overrightarrow{AB} = k\overrightarrow{BC}$,we have:$3 = k(1) \Rightarrow k = 3$.Equating the $\hat{j}$ components: $m + 1 = k(11 - m)$.Substituting $k = 3$: $m + 1 = 3(11 - m)$.$m + 1 = 33 - 3m$.$4m = 32$.$m = 8$.

If the points $(-1, -1, 2), (2, m, 5)$ and $(3, 11, 6)$ are collinear,find the value of $m$.

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