## 3D Coordinate Geometry Quiz-18

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background. Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced..
3D Coordinate Geometry Quiz-18
Q1. The foot of perpendicular from point P(1,3,4) in the plane 2x-y+z+3=0 is:
•  (3,5,-2)
•  (-3,5,2)
•  (3,-5,2)
•  (-1,4,3)
Solution

Q2.If a plane meets the coordinate axes at A,B and C in such a way that the centroid of ∆ABC is at the point (1, 2, 3) the equation of the plane is :
•  $$\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1$$
•  $$\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$$
•  $$\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=\frac{1}{3}$$
•  None of these
Solution

Q3.  The direction cosines l,m,n of two lines are connected by the relations l+m+n=0,lm=0, then the angle between them is :
•  π/3
•  π/4
•  π/2
•  0
Solution

Q4. The centre of sphere passes through four points (0, 0, 0), (0, 2, 0), (1, 0, 0) and (0,0,4) is
•  $$(\frac{1}{2},1,2)$$
•  $$(-\frac{1}{2},1,2)$$
•  $$(\frac{1}{2},1,-2)$$
•  $$(1,\frac{1}{2},2)$$
Solution

Q5.If P is a point in space such that $\stackrel{\to }{\mathrm{OP}}$ is inclined to OX at 45° and OY to 60°, then $\stackrel{\to }{\mathrm{OP}}$ is inclined to OZ at
•  75°
•  60° or 120°
•  75° or 105°
•  255°
Solution

Q6. The equation of the plane through the point (2, 5, -3) perpendicular to the planes x+2y+2z=1 and x-2y+3z=4 is
•  3x-4y+2z-20=0
•  7x-y+5z=30
• x-2y+z=11
•  10x-y-4z=27
Solution

Q7. The ratio in which yz-palne divides the line segment joining (-3,4,-2) and (2,1,3) is:
•  -4:1
•   3 : 2
•  -2∶3
•   1:4
Solution

Q8. A plane which passes through the point (3, 2, 0) and the line $$\frac{(x-3)}{1}=\frac{(y-6)}{5}=\frac{(z-4)}{4}$$ is :
•  x-y+z=1
•  x+y+z=5
•  x+2y-z=0
•  2x-y+z=5
Solution

Q9. The angle between two planes 2x-y+z=6 and x+2y+3z=3 is:
•  $$cos^-1 ⁡(\frac{1}{2} √(\frac{1}{7}))$$
•  $$cos^-1 ⁡(\frac{1}{2} √(\frac{2}{7}))$$
•  $$cos^-1 ⁡(\frac{1}{2} √(\frac{3}{7}))$$
•  $$cos^-1 ⁡(\frac{1}{2} √(\frac{4}{7}))$$
Solution

Q10. A variable plane passes through a fixed point (a,b,c) and meets the coordinate axes in P,Q,R. The locus of the point of intersection of the planes through P,Q,R parallel to the coordinate planes is:
•  $$\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1$$
•  ax+by+cz=1
•  $$\frac{a}{x}+\frac{b}{y}+\frac{c}{z}=-1$$
• ax+by+cz=-1
Solution
(a)

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