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Product Of Two Vectors
Chapter Name : Vector Algebra
Sub Topic Code : 104_12_10_06_03
Topic Name : Product Of Two Vectors
Sub Topic Name : Vector/cross product
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.

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