Let PM be the perpendicular from the point P(1, 2, 3) to xy plane. If OP makes an angle θ with the +ve direction of the z-axis and OM makes an angle φ with the positive direction of x-axis, where O is the origin then ( θ and φ are acute angles)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a, b, c)
P be (x, y, z)
x = r sin θ . cos φ , y = r sin θ sin φ , z = r cos θ
1 = r sin θ . cos φ , 2 = r sin θ sin φ , 3 = r cos θ
1 2 + 2 2 + 3 2 = r 2 sin 2 θ cos 2 φ + r 2 sin 2 θ sin 2 φ + r 2 cos 2 θ
= r 2 sin 2 θ (cos 2 φ + sin 2 φ ) + r 2 cos 2 θ
= r 2 sin 2 θ + r 2 cos 2 θ = r 2
r 2 = 14
r = ± 
sin θ cos φ = + 
, sin θ sin φ = 
,
cos θ = 
(neg. –ve sign)
= 
and tan θ 
= 
tan φ = 2
tan θ = 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems