Vectors and Their Algebra

Name: Vectors and Their Algebra
Author: StemPy Lab

A ship sails 6 kilometres north and then 8 kilometres east. How far is it from the harbour? The distance sailed is one number, but where the ship is needs a size and a direction. In this course you describe a vector by its components and its direction cosines, add and scale vectors, and find the point that divides a line in a given ratio. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

3 lessons, about 1 h 20 min3 simulations10 problems3 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Vectors, components and direction cosines
A vector has a size and a direction. We write it with components along the three axes, find its magnitude with the theorem of Pythagoras, and divide by the magnitude to get a unit vector. The direction cosines are the components of that unit vector.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 2about 25 min
Adding and scaling vectors
Vectors add by the triangle law or the parallelogram law, and in components we add the matching components. Multiplying by a number stretches or flips a vector. The vector from a point $A$ to a point $B$ is found as the position vector of $B$ minus the position vector of $A$ .
1 simulation1 practice question1 Python program3 problems
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Lesson 3about 25 min
Position vectors and the section formula
A point that divides a line segment in the ratio $m : n$ has the position vector $\dfrac{n\vec a + m\vec b}{m + n}$ . The same formula, with $n$ replaced by $-n$ , gives the point that divides the segment externally. The midpoint, the centroid and the fourth vertex of a parallelogram all follow from it.
1 simulation1 practice question1 Python program4 problems1 Python lab1 question set1 note
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Vectors and Their Algebra: Practice Paper

15 questions · 20 min

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Vectors and Their Algebra

Course outline (3 lessons)

Vectors, components and direction cosines

Adding and scaling vectors

Position vectors and the section formula

Test Your Learning

Your teacher

Discussion (0)