Question

Find the point of intersection of the following pair of lines, assuming that the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are not parallel.

$\overrightarrow{r}=\overrightarrow{a}+\mu \overrightarrow{b}$,

$\overrightarrow{r}=\overrightarrow{b}+\gamma \overrightarrow{a}$

• A. a+b.
• B. a-b
• C. a
• D. b

Answer 1

Answer: (A)

a+b.

Given:

vectors $\overline{a},\overline{b}$ are not parallel
$\overline{r}=\overline{a}+\mu \overline{b}$------(1)

$\overline{r}=\overline{b}+\gamma \overline{a}$------(2)

To know the point of intersection , those should be made equal (coefficients)

$\overline{a}+\mu \overline{b}$$=\overline{b}+\gamma \overline{a}$

So from above we get,

$1=\gamma 1=\mu$
Put $\mu =1$ and $\gamma =1$ in any of the equation

we get $\overline{r}=\overline{a}+\overline{b}$

Point of intersection is $\overline{a}+\overline{b}$