SATHEE: 3D Geometry 3 Question 46

3D Geometry 3 Question 46

####46. If $P$ is $(3, 2, 6)$ is a point in space and $Q$ be a point on the line $\vec{r} = (\hat{i} - \hat{j} + 2 \hat{k}) + μ (- 3 \hat{i} + \hat{j} + 5 \hat{k})$ . Then, the value of $μ$ for which the vector $P Q$ is parallel to the plane $x - 4 y + 3 z = 1$ , is

(2009)

(a) $\frac{1}{4}$

(b) $- \frac{1}{4}$

(d) $- \frac{1}{8}$

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Answer:

Correct Answer: 46. (a)

Solution:

Given, $O Q = (1 - 3 μ) \hat{i} + (μ - 1) \hat{j} + (5 μ + 2) \hat{k}$ and $O P = 3 \hat{i} + 2 \hat{j} + 6 \hat{k}$

[where, $O$ is origin]

Now, $P Q = (1 - 3 μ - 3) \hat{i} + (μ - 1 - 2) \hat{j} + (5 μ + 2 - 6) \hat{k}$

$= (- 2 - 3 μ) \hat{i} + (μ - 3) \hat{j} + (5 μ - 4) \hat{k}$

$∵ P Q$ is parallel to the plane $x - 4 y + 3 z = 1$ .

$∴ - 2 - 3 μ - 4 μ + 12 + 15 μ - 12 = 0$

$\Rightarrow 8 μ = 2 \Rightarrow μ = \frac{1}{4}$

3D Geometry 3 Question 46

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3D Geometry 3 Question 46

Answer:

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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