The vertex `A` triangle `A B C` is on the line ` vec r= hat i+ hat j+lambda hat k` and the vertices `Ba n dC` have respective position vectors ` hat ia n d hat jdot` Let `"Delta"` be the area of the triangle and `"Delta"[3//2,sqrt(33)//2]` . Then the range of values of `lambda` corresponding to `A` is `[-8,4]uu[4,8]` b. `[-4,4]` c. `[-2,2]` d. `[-4,-2]uu[2,4]`

Options

A. [-8, -4]cup[4,8]`
B. `[-4,4]`
C. [-2,2]
D. `[-4,-2] cup[2,4]`

Answer

c

Explanation

` triangle=1/2|(hatj +lambdahatk) xx(hati+lambdahatk)|=1/2|=hatk+lambdahati+lambdahatj| =1/2 sqrt(2lambda^(2)+1)`
` Rightarrow 9/4 ge 1/4 (2lambda^(2) +1) ge 33/4`
` or 4 ge lambda^(2)16`
`or 2 ge |lambda|ge 4`