Question

If $\bar{a}$ and $\bar{b}$ represent two non collinear vectors, the equation $\bar{r}=t \bar{a}+(1-t) \bar{b}$ represents

• A. a point 011 the third side of a triangle for which $\bar{a}, \bar{b}$ are two sides, only when $0 \leq t \leq 1$
• B. a point on the line joining the points whose position vectors are $\bar{a}$ and $\bar{b}$
• C. a vector in the plane of $\bar{a}, \bar{b}$ only when $t > 1$
• D. a vector in the plane parallel to the plane of $\bar{a}$ and $\bar{b}$, only when $-1 \leq t \leq 1$

Answer 1

Answer: (A)

We have,
$r=t a+(l-t) b$, where $a$ and $b$ are two non collinear vector, $r-b=t(a-b)$

Clearly, $r$ is a point on the third side of triangle where $a, b$ are two sides of triangle when $t \in[0,1]$