Question

If the position vectors of the points A, B, C be $\mathbf{a},\mspace{6mu}\mathbf{b}$, $\mathbf{3a}\mathbf{-}\mathbf{2b}$ respectively, then the points A, B, C are

• A. Collinear
• B. Non-collinear
• C. Form a right angled triangle
• D. None of these

Answer 1

Answer: (A)

Collinear

Answer 2

Here $\overset{\rightarrow}{AB} = \mathbf{b} - \mathbf{a}$ and $\overset{\rightarrow}{AC} = (3\mathbf{a} - 2\mathbf{b}) - (\mathbf{a}) = - 2(\mathbf{b} - \mathbf{a})$

Therefore, it is of the form $\overset{\rightarrow}{AB} = m\overset{\rightarrow}{AC}.$

Hence A, B, C are collinear.