wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The vector a×(b×c) is

A
Perpendicular to b and parallel to c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Coplanar with b and c and orthogonal to a
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(c) Perpendicular to both b and c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of the above
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B Coplanar with b and c and orthogonal to a
Look its simple.
Let u=a×(b×c)
­­­From the definition of cross product u is perpendicular to a and b×c …. (1)
Now u is perpendicular to b×c.

See the figure. If b and c are the vectors (mentioned in blue) in the plane as shown then b×c will be perpendicular to that plane as shown by orange arrow. This orange arrow is in the direction of b×c
Now from statement 1 we can say that
u is perpendicular to the plane of b×c. The plane perpendicular to the plane of b×c (the orange arrow) is the plane which contains b and c
This implies u lies in the plane of b and c.
Also from the statement (1), u is orthogonal to a (Definition of cross product).
So u is coplanar with b and c and orthogonal to a.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Vector Triple Product
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon