CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let three vectors a,b and c be such that a×b=c, b×c=a and |a|=2. Then which one of the following is not true:

A
a×((b+c)×(bc))=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Projection of a on (b×c) is 2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
[a b c]+[c a b]=8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
|3a+b2c|2=51
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D |3a+b2c|2=51
a×b=c(a×b).c=c.c
[a b c]=|c|2(i)
and (b×c)=aa.(b×c)=a.a
[a b c]=|a|2=4(ii)
|a|=|c|=2

Option: (1)
a×((b+c)×(bc))=a×(b×c+c×b)

=2a×(c×b)=2a×(a)=0

Option: (2)
Projection of a on (b×c)=a.(b×c)|b×c|=|a|2|a|=2

Option: (3)
[a b c]+[c a b]=2[a b c]=8

Option: (4)
|3a+b2c|2
=9a2+b2+4c2+6a.b4b.c12a.c
=9.22+12+4.22+0
=53
a.b=b.c=c.a=0

and [a b c]2=∣ ∣ ∣ ∣a.aa.ba.cb.ab.bb.cc.ac.bc.c∣ ∣ ∣ ∣
16=|a|2 |b|2 |c|2
|b|=1

flag
Suggest Corrections
thumbs-up
12
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Vector Addition
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon