Question

Let $\vec{a} = \hat{i} +2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}-3\hat{j}+\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}-2\hat{k}$ be three vectors. If $\vec{r}$ is a vector such that $\vec{r}\cdot\vec{a} = 0$, $\vec{r}\cdot\vec{b} = -2$ and $\vec{r}\cdot\vec{c} = 6$ then $\vec{r}\cdot(3\hat{i}+\hat{j}+\hat{k})= $

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

When a vector $\vec{r}$ is defined by its dot products with three other non-coplanar vectors, it creates a system of three linear equations. Solving this system gives the components of $\vec{r}$.

Answer 1

The Correct Option is D