CBSE (Commerce) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Write the Ratio in Which Yz-plane Divides the Segment Joining P (−2, 5, 9) and Q (3, −2, 4). - CBSE (Commerce) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).

Solution

\[ \text{ Let the YZ - plane divide the line segment joining points } P\left( - 2, 5, 9 \right) \text { and Q } \left( 3, - 2, 4 \right) \text{ in the ratio k: 1 } . \]

\[ \text{ Using the section formula, the coordinates of the point of intersection are given by }\]

\[\left( \frac{k\left( 3 \right) - 2}{k + 1}, \frac{k\left( - 2 \right) + 5}{k + 1}, \frac{k\left( 4 \right) + 9}{k + 1} \right)\]

\[ \text{ On the YZ - plane, the X - coordinate of any point is zero } . \]

\[ \therefore \frac{k\left( 3 \right) - 2}{k + 1} = 0\]

\[ \Rightarrow 3k - 2 = 0\]

\[ \Rightarrow k = \frac{2}{3}\]

\[ \text{ Thus, the YZ - plane divides the line segment formed by joining the given points in the ratio 2: 3 internally  } . \]

  Is there an error in this question or solution?
Solution Write the Ratio in Which Yz-plane Divides the Segment Joining P (−2, 5, 9) and Q (3, −2, 4). Concept: Direction Cosines and Direction Ratios of a Line.
S
View in app×