MathematicsThe vertices B and C of a Δ ABC lie on the line, , such that BC = 5 units. Then the area of this triangle, given that the point A(1, –1, 2) is.

The vertices B and C of a Δ ABC lie on the line, , such that BC = 5 units. Then the area of this triangle, given that the point A(1, –1, 2) is.

Solution:

‘B’, and ‘C’ lies on the line

…(i)

y = 1
Coordinate of D{3

–2, 1, 4

}
Direction ratio of AD
= {3

–3, 2, 4

–2}
Line AD & Line 4 is perpendicular to each other
So
3( 3λ – 3) + 2 × 0 + 4( 4λ – 2) = 0
⇒ 9λ – 9 + 16λ – 8 = 0
λ =

Coordinate of Δ = {3λ – 2, 1, 4 λ }

Area of ΔABC

AD =

Area of ΔABC

unit square.

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