Dot Product of Two Vectors

Q.

$If\overline{a}.\overline{b}=\overline{a}.\overline{c}and\overline{a}\ne \overline{0},thenwecansaythat\overline{b}=\overline{c}.$

1. True

2. False

Q. Line passing through the points $2\overline{a}+3\overline{b}-\overline{c},3\overline{a}+4\overline{b}-2\overline{c}$ intersects the line passing through the points $\overline{a}-2\overline{b}+3\overline{c},\overline{a}-6\overline{b}+6\overline{c}$ at $P$. Position vector of $P$ is equal to

1. $2\overline{a}+\overline{b}$
2. $\overline{a}+2\overline{b}$
3. $3\overline{a}+4\overline{b}$
4. $\overline{a}-2\overline{b}$