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प्रश्न
If the points (–1, –1, 2), (2, m, 5) and (3,11, 6) are collinear, find the value of m.
उत्तर
Let the given points be A(–1, –1, 2), B(2, m, 5) and C(3, 11, 6).
Then `vec"AB" = (2 + 1)hat"i" + ("m" + 1)hat"j" + (5 - 2)hat"k"`
= `3hat"i" + ("m" + 1)hat"j" + 3hat"k"`
And `vec"AC" = (3 + 1)hat"i" + (11 + 1)hat"j" + (6 - 2)hat"k"`
= `4hat"i" + 12hat"j" + 4hat"k"`.
Since A, B, C, are collinear
We have `vec"AB" = lambda vec"AC"`
i.e., `(3hat"i" + ("m" + 1)hat"j" + 3hat"k") = lambda(4hat"i" + 12hat"j" + 4hat"k")`
⇒ 3 = `4lambda` and m + 1 = `12lambda`
Therefore m = 8.
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