Q90 / 155 · WBJEE 2025 · Mathematics

$\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}, \lambda \vec{b}+4 \vec{c}$ and $(2 \lambda-1) \vec{c}$ are non-coplanar for

  • A
    no value of $\lambda$
  • B
    all except one value of $\lambda$
  • Correct answer
    C
    all except two values of $\lambda$
  • D
    all values of $\lambda$

Solution

for co-planar : $\left|\begin{array}{ccc}1 & 2 & 3 \\ 0 & \lambda & 4 \\ 0 & 0 & 2 \lambda-1\end{array}\right|=0 \Rightarrow \lambda=0, \frac{1}{2}$

Hence, the correct answer is option: 'C'.

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