First slide

Introduction to 3-D Geometry

Question

If O is the origin and the line OP of length r makes an angle $α$ with X-axis and lies in the XY-plane then the coordinates of P are

Moderate

A

$(r \cos α, 0, r \sin α)$
B

$(r \cos α, r \sin α, 0)$
C

$(0, 0, r \cos α)$
D

$(r \sin α, r \cos α, 0)$

Solution

OP lies in XY- plane and makes $α$ angle with X-axis $\Rightarrow$ it makes $\frac{π}{2} - α$ with Y- axis and $\frac{π}{2}$ with Z- axis.
d.c’s of OP are $(l, m, n) = (\cos α, \cos (\frac{π}{2} - α), \cos \frac{π}{2})$
$= (\cos α, \sin α, 0)$ , $P = (l r, m r, n r)$

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