The Dot Product

Name: The Dot Product
Author: StemPy Lab

How much of a push along a ramp does a rope give when it pulls at an angle? Only the part of the force that points along the motion does the work. The dot product measures that part. In this course you find the dot product from components and from the angle. You use it to find angles and to test for right angles. Then you use it for projections and for work done. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The dot product and its rules
The dot product of two vectors is a number: the product of their sizes and the cosine of the angle between them. In components it is the sum of the products of the matching components. Its sign tells us whether the angle is acute, right or obtuse, and its rules let us expand expressions such as $\lvert\vec a + \vec b\rvert^2$ .
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 25 min
Angles and perpendicular vectors
The formula $\cos\theta = \dfrac{\vec a\cdot\vec b}{\lvert\vec a\rvert\lvert\vec b\rvert}$ gives the angle between two vectors. Two non-zero vectors are perpendicular exactly when their dot product is zero. This tests for right angles in triangles, rhombuses and boxes, and it finds the angle between the lines of a solid.
1 simulation1 practice question1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Projections and work done
The projection of $\vec a$ on $\vec b$ is the shadow of $\vec a$ on the line of $\vec b$ . Its signed length is $\dfrac{\vec a\cdot\vec b}{\lvert\vec b\rvert}$ . The work done by a constant force is the dot product of the force and the displacement. The same idea splits any vector into a part along a line and a part across it.
1 simulation1 practice question1 Python program3 problems1 Python lab1 question set1 note
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The Dot Product: Timed Test

10 questions · 25 min

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The Dot Product

Course outline (3 lessons)

The dot product and its rules

Angles and perpendicular vectors

Projections and work done

Test Your Learning

Your teacher

Discussion (0)