Advertisement Remove all ads

Xoz-plane Divides the Join of (2, 3, 1) and (6, 7, 1) in the Ratio - Mathematics

MCQ

XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

Options

  • 3 : 7

  •  2 : 7

  • –3 : 7

  •  –2 : 7

Advertisement Remove all ads

Solution

 −3:7

Let A\[\equiv\](2, 3, 1) and B\[\equiv\]Let the line joining A and B be divided by the xz-plane at point P in the ratio\[\lambda: 1\] 

Then, we have,

P\[\equiv \left( \frac{6\lambda + 2}{\lambda + 1}, \frac{7\lambda + 3}{\lambda + 1}, \frac{\lambda + 1}{\lambda + 1} \right)\]

Since P lies on the xz-plane, the y-coordinate of P will be zero.

\[\therefore \frac{7\lambda + 3}{\lambda + 1} = 0\]
\[ \Rightarrow 7\lambda + 3 = 0\]
\[ \Rightarrow \lambda = \frac{- 3}{7}\]

Hence, the xz-plane divides AB in the ratio \[-\]3 : 7

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 28 Introduction to three dimensional coordinate geometry
Q 8 | Page 23
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×