Product Of Two Vectors
Chapter Name : Vector Algebra |
Sub Topic Code : 104_12_10_06_03 |
Topic Name : Product Of Two Vectors |
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Sub Topic Name : Vector/cross product |
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Introduction
The vector product of two nonzero vectors a? and b?, is denoted by a?xb? and defined as a?xb?=| a?||b?|sin ? nˆ where, ? is the angle between a? and b?, 0 ? ? ? ? and ˆ n is a unit vector perpendicular to both a? and b?, such that a?, b? and nˆ form a right handed system .i.e., The right handed system rotated from a? to b? moves in the direction of nˆ. When the positive x-axis is rotated counter-clockwise into the positive y-axis, a right handed screw would advance in the direction of the positive z-axis.
Pre-Requisites:
• Coordinate Axes • Geometry Basics • Knowledge of displacement, force, pressure, acceleration etc.
Activity:
Observe the direction and force you apply when you open a door/ push a chair/open a can of Jam. Also, observe the acceleration of your car/bus while driving to school.
Real Life Question:
How do you find area of a triangle or a parallelogram?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Scalar Quantity | A scalar is a quantity which can be described by a single number, unlike vectors, tensors, etc. which is described by several numbers which describe magnitude and direction. |
| Vector Quantity | A vector is a geometric object that has magnitude and direction and can be added to other vectors according to vector algebra. |
| Magnitude | Magnitude is a term for the size or length of a vector. |
| Direction | It is the Relative direction, for instance left, right, forward, backwards, up, and down. |
| Vector Product | The vector product of two nonzero vectors a? and b?, is denoted by a?xb? and defined as a?xb?=| a?||b?|sin ? nˆ. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Screw | Check the right handed screw rule. |
Real life uses :
An airplane landing in a crosswind is a real-world example of vector addition. When a strong wind blows across a runway, the pilot must aim the plane into the wind so that a component of the plane's velocity will cancel the crosswind. The key is to get the resultant velocity vector to point directly along the runway.
Practical examples around us
| Examples | Explainations |
|---|---|
| Breathing | Your diaphragm muscles exert a force that has a magnitude and direction. |
| Walking | You walk at a velocity of around 6 km/h in the direction of your park. |
What you learn in Theory:
We learn how to find the cross product of two vectors.
What you learn in Practice:
We learn how to find the area of a triangle and a parallelogram using cross product.