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The vertices B and C of a DeltaABC lie o...

The vertices B and C of a `DeltaABC` lie on the line, `(x+2)/(3)=(y-1)/(0)=(z)/(4)` such that BC=5 units. Then, the area (in sq units) of this triangle, given that the point A(1, -1, 2) is

A

`2 sqrt(34)`

B

`sqrt(34)`

C

6

D

`5 sqrt(17)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Ar (ABC) = (1)/(2) xx BC xx AN`
`AN = AD sin theta`
`overline(AD) = 3 hat(i) - 2 hat(j) + 2 hat(k)`
`vec(l) = 3 hat(i) + 4 hat(k)`
`AD sin theta = |overline(AD) xx hat(l)|`
`= (|(2 hat(i) - 2 hat(j) + 2 hat(k)) xx (3 hat(i) + 4 hat(k))|)/(5) = (|- 8 hat(i) + 6 hat(j) + 6 hat(k)|)/(5) = (sqrt(136))/(5)`
`Ar (ABC) = (1)/(2) xx 5 xx sqrt((136)/(5)) = sqrt(34)`
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