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.

# 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.

1. A
2. B
3. C
6
4. D

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### 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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