TS EAMCET · Maths · Vector Algebra
If \(\mathbf{a}\) and \(\mathbf{b}\) represent two non collinear vectors, the equation \(\mathbf{r}=t \mathbf{a}+(\mathrm{l}-t) \mathbf{b}\) represents
- 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 \(-1 \leq t \leq 1\)
Answer & Solution
Correct Answer
(A) a point on the third side of a triangle for which \(a, b\) are two sides, only when \(0 \leq t \leq 1\)
Step-by-step Solution
Detailed explanation
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…
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