0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

# Show that a.(b×c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, a, b and c.

Solution
Verified by Toppr

#### A parallelopiped with origin O and sides a,b, and c is shown in the following figure.Volume of parallelopiped=abcLet ^n be a unit vector perpendicular to both →b and →c. Hence ^n and →c have the same direction.Therefore, →b×→c=bcsinθ ^n=bc^n→a.(→b×→c)=a.(bc^n) =abc= Volume of parallelopiped

12
Similar Questions
Q1
Show that a.(b×c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, a, b and c.
View Solution
Q2
Show that a.(b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.
View Solution
Q3

Show that a. (b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors, a, b and c.

View Solution
Q4
If a, b, c are three non-coplanar vectors such that volume of parallelopiped formed with a, b, c, as coterminous edges is equal to volume of parallelopiped formed with a×b,b×c,c×a as coterminous edges, then:
View Solution
Q5

Show that a.(b×c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors, a, b and c.

View Solution