Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
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

What is the formula of triple scalar product and how it is derived?

What is the formula of triple scalar product and how it is derived?

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear student,

The scalar triple product

The scalar triple product of three vectors a, b, and c is (a × b) c. It is a scalar product because it evaluates to a single number . The scalar triple product is important because its absolute value |(a × b) c| is the volume of the parallelepiped spanned by a, b, and c (i.e., the parallelepiped whose adjacent sides are the vectors a, b, and c).

 

PIC.

This results from simple geometry. The volume is the area of the base times the height. We already know the area of the parallelogram base: ||a × b||. The height is the component of c in the direction normal to the base, i.e., in the direction of a × b. Hence the height is ||c|| | cos ?|, where ? is the angle between c and a × b. (Why do we need the absolute value? cos ? would be negative if ? > π/2.)

The volume of the parallelepiped is therefore

Volume = ||a × b|| ||c|| | cos ?| = |(a × b) c|.

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free