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

If 2^i+3^j+4^k and ^i^j+^k are two adjacent sides of a parallelogram, then the area of the parallelogram will be

A
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Cannot be calculated from the given data
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
We know that when two adjacent sides of a parallelogram are given, the area of the parallelogram is given by the magnitude of the cross product of these two vectors. Here two given sides are 2^i+3^j+4^k and ^i^j+^k
So their cross product will be given by the following determinant
∣ ∣ ∣^i^j^k234111∣ ∣ ∣
= ^i((3×1)(4×1)^j(2×1)(4×1)+^k(2×1)(3×1))
=7^i+2^j5^k
Now the modulus of this cross product i.e. 7^i+2^j5^k, will give you the area of the parallelogram.
|7^i+2^j5^k|=(7)2+(2)2+(5)2
=49+4+25
=78
Which is nothing but the area of the given parallelogram


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Test for Collinearity of 3 Points or 2 Vectors
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon