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

• Correct answer
  A

  a point on the third side of a triangle for which $a, b$ are two sides, only when $0 \leq t \leq 1$
• B

  a point on the line joining the points whose position vectors are a and b
• C

  a vector in the plane of $\mathrm{a}, \mathrm{b}$ only when $t>1$
• D

  a vector in the plane parallel to the plane of a and b, only when $-1 \leq t \leq 1$

Solution

We have, $\mathbf{r}=t \mathbf{a}+(\mathbf{l}-t) \mathbf{b}$, where $\mathbf{a}$ and $\mathbf{b}$ are two non collinear vector, $\mathbf{r}-\mathbf{b}=t(\mathbf{a}-\mathbf{b})$
Clearly, $\mathbf{r}$ is a point on the third side of triangle where $\mathbf{a}, \mathbf{b}$ are two sides of triangle when $t \in[0,1]$

Hence, the correct answer is option: 'A'.