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

If the lines:
2x3=2y33k=z42 and 22x5k=y+42=5z4 are perpendicular then find the value of k.

Open in App
Solution

The direction vectors of the lines represented in standard form x23=y1.51.5k=z42 and x12.5k=y+42=z54 are
n1=3^i+1.5k^j+2^k
n2=2.5k^i+2^j4^k
Now, as the lines are perpendicular, their dot product is 0
n1n2=0
(3^i+1.5k^j+2^k)(2.5k^i+2^j4^k)=0
7.5k+3k8=0
10.5k=8
k=1621
This is the required value of k.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Relative Motion
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon