Test Index

Systems of Particles and Rotational Motion

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Question : 5
Total: 33
Show that
→
a
.(
→
b
×
→
c
) is equal in magnitude to the volume of the parallelepiped formed on the three vectors,
→
a
,
→
b
 and
→
c
Solution:  
Let a parallelopiped be formed on the three vectors
→
OA
=
→
a
,
→
OB
=
→
b
and
→
OC
=
→
c

Now,
→
b
×
→
c
=bc‌sin‌90°‌
^
n
=bc
^
n

where
^
n
 is unit vector along
→
OA
 perpendicular to the plane containing
→
b
 and
→
c
.
Now
→
a
.(
→
b
×
→
c
) =
→
a
.bc
^
n
=(a)(bc)‌cos‌0°=abc
which is equal in magnitude to the volume of the parallelopiped.
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