Question

Two vectors are given by $\text{a=-2i+j-3k}$ and $\text{b=5i+3j-2k}$. if $\text{3a+2b-c=0}$ then third vector $\text{c}$ is

Answer 1

Step 1: Given:

Vector $\text{a=-2i+j-3k}$,

Vector $\text{b=5i+3j-2k}$

Step 2: Calculate value of vector $\text{c}$:

$\text{3a+2b-c=0}$

Substitute $\text{a=-2i+j-3k}$ and $\text{b=5i+3j-2k}$ in above expression.

$$\begin{gathered} \text{3}\left(-\text{2i}+\text{j}-\text{3k}\right)+2\left(\text{5i}+\text{3j}-\text{2k}\right)-\text{c}=0 \\ \text{c=-6i+3j-9k+10i+6j-4k} \\ \text{=4i+9j-13k} \end{gathered}$$

Hence, the required vector c is $\text{4i+9j-13k}$.