# Find the Vector Equation of the Plane Passing Through the Points A(1, 0, 1), B(1, –1, 1) and C(4, –3, 2). - Mathematics and Statistics

Sum

Find the vector equation of the plane passing through the points A(1, 0, 1), B(1, –1, 1) and C(4, –3, 2).

#### Solution

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

Concept: Plane - Equation of Plane Passing Through the Given Point and Perpendicular to Given Vector
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