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

Vectors a, b and c are of the same length and when taken pairwise, they form equal angles. If a=^i+^j and b=^j+^k, then vector c can be

A
^i+^k
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
13^i43^j13^k
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
13^i+43^j13^k
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
^i+2^j+^k
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 13^i+43^j13^k
Let c=x^i+y^j+z^k
Then |a|=|b|=|c|x2+y2+z2=2
It is given that the angles between the vectors taken in pairs are equal, say θ.
Therefore, cos θ=a.b|a||b|=0+1+022=12
a.c|a||c|=12 and b.c|b||c|=12
x+y2=12 and y+z2=12
x+y=1 and y+z=1
y=1x and z=1y=1(1x)=x

x2+y2+z2=2x2+(1x)2+x2=2
(3x+1)(x1)=0
x=1,13
Now, y=1x
y=0 for x=1 and y=43 for x=13
Hence, c=^i+^k or c=13^i+43^j13^k

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon