1
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1
Out of Syllabus

If the lines $${{x - 1} \over 1} = {{y - 2} \over 2} = {{z + 3} \over 1}$$ and $${{x - a} \over 2} = {{y + 2} \over 3} = {{z - 3} \over 1}$$ intersect at the point P, then the distance of the point P from the plane $$z = a$$ is :

A
28
B
22
C
10
D
16
2
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1

The shortest distance between the lines $${{x - 1} \over 2} = {{y + 8} \over -7} = {{z - 4} \over 5}$$ and $${{x - 1} \over 2} = {{y - 2} \over 1} = {{z - 6} \over { - 3}}$$ is :

A
$$2\sqrt3$$
B
$$3\sqrt3$$
C
$$4\sqrt3$$
D
$$5\sqrt3$$
3
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The foot of perpendicular of the point (2, 0, 5) on the line $${{x + 1} \over 2} = {{y - 1} \over 5} = {{z + 1} \over { - 1}}$$ is ($$\alpha,\beta,\gamma$$). Then, which of the following is NOT correct?

A
$$\frac{\alpha}{\beta}=-8$$
B
$$\frac{\alpha \beta}{\gamma}=\frac{4}{15}$$
C
$$\frac{\beta}{\gamma}=-5$$
D
$$\frac{\gamma}{\alpha}=\frac{5}{8}$$
4
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The shortest distance between the lines $$x+1=2y=-12z$$ and $$x=y+2=6z-6$$ is :

A
3
B
$$\frac{5}{2}$$
C
$$\frac{3}{2}$$
D
2
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