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

A point “P” is located in three dimensional coordinate plane such that the angles made by OP with positive direction of X - axis is 30 and Y- axis is 60 then find the angle made by OP with positive direction of Z - axis, where “O” is origin.

A
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
45
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
60
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
90
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 90
We know that cos of the angles made by a line segment with the positive direction of axes give us the direction cosines. Let the angle made with Z - axis be γ , where 0 γπ
So, the direction cosines of OP will be cos30 ,cos60,cosγ
We know one property of direction cosines.
if the direction cosines of a line are l, m and n then
l2+m2+n2=1
So,(cos30)2+(cos60)2+(cosγ)2=1
Or,(32)2+(cosγ)2=1
Or,(cosγ)2=0
Or cosγ=0
Since 0γπ the only possible value γ can have is π2 radians.
So, γ=90

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Direction Cosines and Direction Ratios
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon