Question

If \(\vec{a},\,\vec{b},\,\vec{c}\) are non-coplanar vectors. If the three points \[ \lambda \vec{a} - 2\vec{b} + \vec{c},\quad 2 \vec{a} + \lambda\vec{b} - 2\vec{c},\quad 4\vec{a} + 7\vec{b} - 8\vec{c} \] are collinear, then \(\lambda = \,?\)

• A. \(-1\)
• B. \(-2\)
• C. \(2\)
• D. \(1\)

Hint:

For collinearity, use \(\vec{PQ} \times \vec{PR} = \vec{0}\) or check if one vector is a scalar multiple of the other.
- Non-coplanar \(\vec{a},\vec{b},\vec{c}\) ensures no degeneracy in the cross-product equations.

Answer 1

The Correct Option is D

N/A