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प्रश्न
Find the vector equation of the plane passing through the points A(1, 0, 1), B(1, –1, 1) and C(4, –3, 2).
बेरीज
उत्तर
Let the p.v. of points A(1, 0, 1), B(1, –1, 1) and C(4, –3, 2) be
`veca = bari + bark`, `barb = bari - barj + bark` and `barc = 4bari - 3barj + 2bark`
`barb-bara = -barj`, `barc-bara = 3bari - 3barj + bark`
`(barb-bara)xx(barc-bara) = |(bari,barj,bark),(0,-1,0),(3,-3,1)| = -bari + 3bark`
Equation of plane through A, B, C in vector form is
`(barr-bara).[(barb-bara)xx(barc-bara)] = 0`
`(barr-bara).(-bari + 3bark) = 0`
`barr.(-bari+3bark) = (bari+bark).(-bari + 3bark) = -1+3 = 2`
∴ `barr.(-bari + 3bark) = 2`
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