Vectors and Scalars
Simple Explanation
A scalar quantity has only a size (magnitude) — like mass, time, or temperature. A vector quantity has both a size and a direction — like displacement, velocity, or force. Vectors are usually drawn as arrows: the length of the arrow shows the magnitude, and the way it points shows the direction.
Why Do We Need It?
Almost every quantity in this chapter — displacement, velocity, acceleration — is a vector, so knowing how to handle direction correctly, right from the start, is essential; forgetting it is one of the most common sources of wrong answers in mechanics.
Worked Example
Add two vectors acting in a straight line
A boat's engine pushes it forward at 6 m/s (east) while a current pushes it at 2 m/s (west). Find the resultant velocity.
Why Does This Work?
Because a vector already encodes direction as a sign (or an angle), adding two vectors that act along the same line is exactly the same as adding signed numbers — opposing directions partially cancel, matching directions reinforce.
Real-Life Example
A plane flying into a headwind
An aircraft cruises at 250 m/s but flies directly into a 30 m/s headwind.
The plane's velocity relative to the ground is the vector sum of its own velocity and the wind's velocity — here, 250 − 30 = 220 m/s, since the wind vector points opposite to the plane's motion.
Practice
Which of these is a vector quantity?
EasyTwo forces act on an object along the same line: 15 N to the right and 9 N to the left. Find the resultant force. (Give the size only, in newtons.)
MediumCommon mistake
Adding vector magnitudes directly without accounting for direction — 6 m/s and 2 m/s acting in opposite directions do NOT add to 8 m/s; direction has to be built into the addition.
Quick Review
- Scalars have magnitude only; vectors have magnitude AND direction.
- Vectors are drawn as arrows — length shows size, arrowhead shows direction.
- Vectors along the same line add like signed numbers; opposite directions partially cancel.