SATHEE: 3D Geometry 3 Question 22

3D Geometry 3 Question 22

####22. The plane which bisects the line segment joining the points $(- 3, - 3, 4)$ and $(3, 7, 6)$ at right angles, passes through which one of the following points?

(2019 Main, 10 Jan II)

(a) $(4, - 1, 7)$

(b) $(2, 1, 3)$

(d) $(4, 1, - 2)$

Show Answer

Answer:

(d)

Solution:

Let the given points be $A (- 3, - 3, 4)$ and $B (3, 76)$ .

Then, mid-point of line joining $A, B$ is

$P \frac{- 3 + 3}{2}, \frac{- 3 + 7}{2}, \frac{4 + 6}{2} = P (0, 2, 5)$

$∵$ The required plane is perpendicular

bisector of line joining $A, B$ , so direction ratios of normal to the plane is proportional to the direction ratios of line joining $A, B$ .

So, direction ratios of normal to the plane are $6, 10, 2$ .

$[∵$ DR’s of $A B$ are $3 + 3, 7 + 3, 6 - 4$ , i.e. $6, 10, 2]$

Now, equation of plane is given by

$\begin{aligned} a (x - x_{1}) + b (y - y_{1}) + c (z - z_{1}) & = 0 \\ 6 (x - 0) + 10 (y - 2) + 2 (z - 5) & = 0 \end{aligned}$

$[∵ P (0, 2, 5)$ line on the plane $]$

$\Rightarrow 3 x + 5 y - 10 + z - 5 = 0$

$\Rightarrow 3 x + 5 y + z = 15$

On checking all the options, the option $(4, 1, - 2)$ satisfy the equation of plane (i).

3D Geometry 3 Question 22

Answer:

Solution:

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3D Geometry 3 Question 22

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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