The ratio in which the plane r- i-2j-3k-17 divides the line joining the points -2i-4j-7k- and 3i-5j-8k- is-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Section Formula

The ratio in ...

Question

The ratio in which the plane $\to r \cdot (\to i - 2 \to j + 3 \to k) = 17$ divides the line joining the points $- 2 \to i + 4 \to j + 7 \to k$ and $3 \to i - 5 \to j + 8 \to k$ is-

1 : 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 : 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 : 10

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $3 : 10$
Equation of plane in cartesian form is, $x - 2 y + 3 z - 17 = 0$ ..... $(1)$
Assume this plane $(1)$ divide the line segment joining the points $(- 2, 4, 7)$ and $(3, - 5, 8)$ in $m : n$ ratio
Therefore, $\frac{m}{n} = \frac{- 2 - 2 (4) + 3 (7) - 17}{3 - 2 (- 5) + 3 (8) - 17} = \frac{- 3}{10} < 0$
Hence, plane (1) divides the given line segment externally $3 : 10$

Suggest Corrections

Similar questions

Q. The distance between the line

\to r = 2 \to i - 2 \to j + 3 \to k + λ (\to i - \to j + 4 \to k)

and the plane

\to r \cdot (\to i + 5 \to j + \to k) = 5

Q. The vectors

2 \to i + 3 \to j + 4 \to k, 3 \to i + 2 \to j - 3 \to k

, and

5 \to i + 5 \to j + \to k

form:

Q. P,Q,R and S are four points with the position vectors

3 \to i - 4 \to j + 5 \to k, 4 \to k, - 4 \to i + 5 \to j + \to k a n d - 3 \to i + 4 \to j + 3 \to k

respectively. Then the line PQ meets the line RS at the point

P,Q,R and S are four points with the position vectors, $3 \to i - 4 \to j + 5 \to k, 4 \to k, - 4 \to i + 5 \to j + \to k and - 3 \to i + 4 \to j + 3 \to k$ respectively. Then the line PQ meets the line RS at the point

Q. If

3 \to i + 2 \to j + 8 \to k

and

2 \to i + x \to j + \to k

are at right angles, then

x =

Join BYJU'S Learning Program

The ratio in which the plane →r⋅(→i−2→j+3→k)=17 divides the line joining the points −2→i+4→j+7→k and 3→i−5→j+8→k is-

The ratio in which the plane $\to r \cdot (\to i - 2 \to j + 3 \to k) = 17$ divides the line joining the points $- 2 \to i + 4 \to j + 7 \to k$ and $3 \to i - 5 \to j + 8 \to k$ is-