Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        PROOF THAT THE MAGNITUDE OF THE CROSS PRODUCT IS THE AREA OF THE PARALLELOGRAM`
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
We define the cross product of two three-dimensional vectors a and b by the requirements:

a × b is a vector that is perpendicular to both a and b.
||a × b|| is the area of the parallelogram spanned by a and b (i.e. the       parallelogram whose adjacent sides are the vectors a and b).
The direction of a×b is determined by the right-hand rule. (This means       that if we curl the fingers of the right hand from a to b, then the thumb       points in the direction of a × b.)

From simple trigonometry, we can calculate that the area of the parallelogram spanned by a and b is

||a|| ||b|| sin θ,

where θ is the angle between a and b. (One can view the parallelogram as having a base of length ||b|| and perpendicular height ||a|| sin θ, as pictured below.)

This formula shows that the magnitude of the cross product is largest when a and b are perpendicular. On the other hand, if a and b are parallel or if either vector is the zero vector, then the cross product is the zero vector. (It is a good thing that we get the zero vector so that the above definition still makes sense. If the vectors are parallel or one vector is the zero vector, then there is not a unique line perpendicular to both a and b. But since there is only one vector of zero length, the definition still uniquely determines the cross product.)

All the best.
Win exciting gifts by                  answering the questions on Discussion Forum. So help      discuss     any       query   on askiitians forum and become an Elite      Expert   League      askiitian.

Sagar Singh
B.Tech, IIT Delhi

```
6 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Vectors

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details
• Statistics and Probability
• OFFERED PRICE: Rs. 636
• View Details