## 3D Coordinate Geometry Quiz-17

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-17
Q1. The plane of intersection of spheres x2+y2+z2+2x+2y+2z=2 and 2x2+2y2+2z2+4x+2y+4z=0 is:
•  Parallel to xz-plane
•  Parallel to y-axis
•  y=0
•  None of these
Solution

Q2.The point of intersection of the lines $$\frac{(x-1)}{2}=\frac{(y-2)}{3}=\frac{(z-3)}{4} and \frac{(x-4)}{5}=\frac{(y-1)}{2} z$$ is :
•  (0, 0, 0)
•  (1, 1, 1)
•  (-1,-1,-1)
•  (1,2,3)
Solution

Q3.  The cartesian equation of the plane $\stackrel{\to }{r}$=(s-2t) $\stackrel{^}{i}$+(3-t) $\stackrel{^}{j}$+(2s+t)$\stackrel{^}{k}$, is:
•   2x-5y-z-15=0
•  2x-5y+z-15=0
•  2x-5y-z+15=0
•  2x+5y-z+15=0
Solution
(c)

Q4. The direction cosines l,m,n of two lines are connected by the relation l+m+n=0, lm=0, then the angles between them is
•  π/3
•  π/4
•  π/2
•  0
Solution

Q5. The angle between the line $$\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$$ and the plane 3x+2y-3z=4 is
•  45°
•
•  $$cos^-1(\frac{24}{(√29 √22)})$$
•  90°
Solution

Q6. The angle between the lines $$\frac{(x-2)}{3}=\frac{(y+1)}{-2},z=2$$ and $$\frac{(x-1)}{1}=\frac{(2y+3)}{3}=\frac{(z+5)}{2}$$ is
•  π/2
•  π/3
• π/6
•  None of these
Solution
(a)

Q7.The intercepts of the plane 2x-3y+4z=12 on the coordinate axes are given by :
•  3,-2,15
•  6,-4,3
•  6,-4,-3
•  2,-3,4
Solution

Q8. The value of k such that $$\frac{(x-4)}{1}=\frac{(y-2)}{1}=\frac{(z-k)}{2}$$ lies in the plane 2x-4y+z=7, is:
•   7
•  -7
•   No real value
•  4
Solution

Q9. The equation of the plane which passes through the point (2, -3, 1) and perpendicular to the line joining points (3,4,-1) and (2,-1,5), is:
•  x+5y-6z+19=0
•  x-5y+6z-19=0
•  x+5y+6z+19=0
•  x-5y-6z-19=0
Solution
(a)

Q10. In ∆ABC and mid points of the sides AB,BC and CA are respectively (1,0,0), (0,m,0) and (0,0,n) Then, $$\frac{(AB^2+BC^2+CA^2)}{(l^2+m^2+n^2)}$$ is equal to :
•  2
•  4
•  8
• 16
Solution

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