The vertex A of triangle ABC is on the line r = i + j + λk and the vertices B & C have respective position vectors i and j. ​

Question

The vertex A of triangle ABC is on the line \(\vec r = \hat i + \hat j + \lambda \hat k\) and the vertices B & C have respective position vectors \(\hat i\) and \(\hat j\). Let \(\triangle\) be the area of the triangle and \(\triangle \in \left[\frac 32, \frac{\sqrt {33}}2\right]\), then the range of values of λ corresponding to A is

(a) [–8, –4] \(\cup\) [4, 8]

(b) [–4, 4]

(c) [–2, 2]

(d) [–4, –2] \(\cup\) [2, 4]

Answer 1

Correct option is (d) [–4, –2] \(\cup\) [2, 4]