Vectors: Adding, Subtracting and Resolving

Name: Vectors: Adding, Subtracting and Resolving
Author: StemPy Lab

You walk 3 km east and then 4 km north. How far are you from the start? The answer is 5 km, and not 7 km. In this course we learn why. We separate scalars from vectors, we add and subtract vectors with arrows and with numbers, and we split any vector into two parts along the axes, which makes hard problems easy.

3 lessons, about 1 h 30 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Scalars and vectors
A scalar has a size only. A vector has a size and a direction, and adds by the triangle rule. Multiplying a vector by a number changes its length, and a negative number also turns it round. A unit vector only shows a direction. Displacement is a vector, but distance is a scalar.
1 simulation2 practice questions1 Python program3 problems1 question set
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Lesson 2about 30 min
Adding and subtracting vectors
Vectors add head to tail (the triangle law), or as the diagonal of a parallelogram. The size of the sum is $R = \sqrt{A^2 + B^2 + 2AB\cos\theta}$ , where $\theta$ is the angle between the vectors, so it lies between $|A - B|$ and $A + B$ . To subtract a vector, add its opposite.
1 simulation2 practice questions1 Python program5 problems1 Python lab
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Lesson 3about 30 min
Resolving vectors and unit vectors
We split a vector into an $x$ part and a $y$ part: $A_x = A\cos\theta$ and $A_y = A\sin\theta$ . With the unit vectors $\hat{i}$ and $\hat{j}$ , $\vec{A} = A_x\hat{i} + A_y\hat{j}$ . To add vectors, add the $x$ parts and the $y$ parts separately. The signs of the parts tell you which quarter the vector points into.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Vectors: Practice Paper

15 questions · 20 min

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Vectors: Adding, Subtracting and Resolving

Course outline (3 lessons)

Scalars and vectors

Adding and subtracting vectors

Resolving vectors and unit vectors

Test Your Learning

Your teacher

Discussion (0)