Correct! \(\vec{A} = \hat{i} - \hat{j}\), \(\vec{B} = - 2 \hat{i} + 3 \hat{j}\) and \(\vec{C} = 2 \hat{i} + \hat{j}\)

So, \(3 \vec{A} = 3 \hat{i} - 3 \hat{j}\), \(- 2\vec{B} = 4 \hat{i} - 6 \hat{j}\) and \(4 \vec{C} = 8 \hat{i} + 4\hat{j}\). We just have to add all these three vectors.

So, \(3 \vec{A} = 3 \hat{i} - 3 \hat{j}\), \(- 2\vec{B} = 4 \hat{i} - 6 \hat{j}\) and \(4 \vec{C} = 8 \hat{i} + 4\hat{j}\). We just have to add all these three vectors.

Up to now, we have talked about vectors abstractly. Let us now look at the use of vectors in Physics. Position is a vector. For example, if an object A is located at position P as shown, we can write its position vector as \(\vec{r}_A\).

Velocity and acceleration are just time-derivatives of position, so, they are also vectors.

Velocity and acceleration are just time-derivatives of position, so, they are also vectors.