3D Coordinate Geometry Quiz-20

 

3D Coordinate Geometry Quiz-20

Dear Readers,

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..

Q1. The angle between a line whose direction ratios are in the ratio 2:2:1 and a line joining (3, 1, 4) to (7, 2, 12) is:

•  $$\(cos^-1⁡(\frac{2}{3})\)
•  $$\(cos^-1⁡(-\frac{2}{3})\)
•  $$\(tan^-1⁡(\frac{2}{3})\)
•  None of these

Solution

Q2.The length of perpendicular from Q(1,6,3) to the line $$\(\frac{x}{1}=\frac{(y-1)}{2}=\frac{(z-2)}{3} \) is :

•  3
•  √11
•  √13
•  5

Solution

Q3.  The direction cosines of the line passing through P(2,3,-1) and the origin are :

•   $$\(\frac{2}{√14},\frac{-3}{√14},\frac{1}{√14}\)
•  $$\(\frac{2}{√14},\frac{-3}{√14},\frac{1}{√14}\)
•  $$\(\frac{-2}{√14},\frac{-3}{√14},\frac{1}{√14}\)
•  $$\(\frac{2}{√14},\frac{-3}{√14},\frac{-1}{√14}\)

Solution

Q4. The length of the perpendicular drawn from (1, 2, 3) to the line$$\(\frac{(x-6)}{3}=\frac{(y-7)}{2}=\frac{(z-7)}{-2}\) is

•  4
•  5
•  6
•  7

Solution

Q5. The angles between two planes x+2y+2z=3 and -5x+3y+4z=9 is

•  $$\(cos^-1⁡(\frac{9√2}{20})\)
•  $$\(cos^-1⁡(\frac{3√2}{5})\)
•  $$\(cos^-1⁡(\frac{3√2}{10})\)
•  $$\(cos^-1⁡(\frac{19√2}{30})\)

Solution
 

Q6. If (2,3,5) is one end of a diameter of the sphere x²+y²+z²-6x-12y-2z+20=0, then
the coordinates of the other end of the diameter are

•  (4,9,-3)
•  (4,-3,3)
• (4, 3, 5)
•  (4,3,-3)

Solution

Q7. The points (5,-4,2),(4,-3,1),(7,-6,4) and (8,-7,5) are the vertices of:

•  A rectangle
•  A square
•  A parallelogram
•  None of these

Solution

Q8. The shortest distance from the point (1,2,-1) to the surface of the sphere x²+y²+z²=54 is :

•  3√6
•  2√6
•  √6
•  2

Solution

Q9.

•  (1)and (2)
•  (2) and (3)
•  (3) and (1)
•  (1), (2) and (3)

Solution

Q10. If the foot of the perpendicular from (0, 0, 0) to a plane is (1, 2, 2), then the equation of the plane is :

•  -x+2y+8z-9=0
•  x+2y+2z-9=0
•  x+y+z-5=0
• x+2y-3z+1=0

Solution