Question

If $\vec{a} = \vec{i} + \vec{j} + \vec{k}$, $\vec{b} = 4\vec{i} + 3\vec{j} + 4\vec{k}$ and $\vec{c} = \vec{i} + \alpha\vec{j} + \beta\vec{k}$ are linearly dependent vectors and $|\vec{c}| = \sqrt{3}$, then:

• A. $\alpha = 1, \beta = -1$
• B. $\alpha = 1, \beta = 1$
• C. $\alpha = -1, \beta = -1$
• D. $\alpha = 2, \beta = 1$

Hint:

Linear dependency of three vectors in $\mathbb{R}^3$ is equivalent to coplanarity. Always set the determinant to $0$.

Answer 1

The Correct Option is B