JEE Main 2019 (Online) 10th January Evening Slot | 3D Geometry Question 174 | Mathematics

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

On which of the following lines lies the point of intersection of the line, $${{x - 4} \over 2} = {{y - 5} \over 2} = {{z - 3} \over 1}$$ and the plane, x + y + z = 2 ?

$${{x - 4} \over 1} = {{y - 5} \over 1} = {{z - 5} \over { - 1}}$$

$${{x - 2} \over 2} = {{y - 3} \over 2} = {{z + 3} \over 3}$$

$${{x - 1} \over 1} = {{y - 3} \over 2} = {{z + 4} \over { - 5}}$$

$${{x + 3} \over 3} = {{4 - y} \over 3} = {{z + 1} \over { - 2}}$$

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

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 ?

(2, 1, 3)

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

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

($$-$$ 2, 3, 5)

JEE Main 2019 (Online) 10th January Morning Slot

MCQ (Single Correct Answer)

-1

The plane passing through the point (4, –1, 2) and parallel to the lines $${{x + 2} \over 3} = {{y - 2} \over { - 1}} = {{z + 1} \over 2}$$ and $${{x - 2} \over 1} = {{y - 3} \over 2} = {{z - 4} \over 3}$$ also passes through the point -

(1, 1, $$-$$ 1)

(1, 1, 1)

($$-$$ 1, $$-$$ 1, $$-$$1)

($$-$$ 1, $$-$$ 1, 1)

JEE Main 2019 (Online) 10th January Morning Slot

MCQ (Single Correct Answer)

-1

Let A be a point on the line $$\overrightarrow r = \left( {1 - 3\mu } \right)\widehat i + \left( {\mu - 1} \right)\widehat j + \left( {2 + 5\mu } \right)\widehat k$$ and B(3, 2, 6) be a point in the space. Then the value of $$\mu $$ for which the vector $$\overrightarrow {AB} $$ is parallel to the plane x $$-$$ 4y + 3z = 1 is -

$${1 \over 8}$$

$${1 \over 2}$$

$${1 \over 4}$$

$$-$$ $${1 \over 4}$$

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