3D Coordinate Geometry Quiz-19

3D Coordinate Geometry Quiz-19

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 projection of the line joining the points (3, 4, 5) and (4, 6, 3) on the line joining the points
(-1, 2 4) and (1, 0, 5) is:

•   4/3
•   2/3
•  -4/3
•   1/2

Solution

Q2.A equation of the plane passing through the points (3, 2, -1), (3, 4, 2) and (7, 0, 6) is 5x+3y-2z=λ, where λ is:

•  23
•  21
•  19
•  27

Solution

Q3.  The equation of the line of intersection of planes 4x+4y-5z=12, 8x+12y-13z=32 can be written as :

•  $$\(\frac{(x-1)}{2}=\frac{(y+2)}{-3}=\frac{z}{4}\)
•  $$\(\frac{(x-1)}{2}=\frac{(y-2)}{3}=\frac{z}{4}\)
•  $$\(\frac{x}{2}=\frac{(y+1)}{3}=\frac{(z-2)}{4}\)
•  $$\(\frac{x}{2}=\frac{y}{3}=\frac{(z-2)}{4} \)

Solution

Q4. The cosine of the angle A of the triangle with verities A(1,-1,2),B(6,11,2),C(1,2,6) is

•  63/65
•  36/65
•  16/65
•  13/64

Solution

Q5.The distance of the point A(-2,3,1) from the line PQ through P(-3,5,2) which make equal angles with the axes is:

•  2/√3
•  √(14/3)
•  16/√3
•  5/√3

Solution
 

Q6. There is point P(a,a,a) on the line passing through the origin and equally inclined with axes. The equation of plane
perpendicular to OP and passing through P cuts the intercepts on axes. The sum of whose reciprocals is:

•  a
•  3/2a
• 3a/2
•  1/a

Solution

Q7. The equation of the line passing through the point (3,0,-4) and perpendicular to the plane 2x-3y+5z-7=0 is :

•  $$\(\frac{(x-2)}{3}=\frac{y}{-3}=\frac{(z+4)}{5}\)
•  $$\(\frac{(x-3)}{2}=\frac{y}{-3}=\frac{(z-4)}{5}\)
•  $$\(\frac{(x-3)}{2}=\frac{(-y)}{3}=\frac{(z+4)}{5}\)
•  $$\(\frac{(x+3)}{2}=\frac{y}{3}=\frac{(z-4)}{5}\)

Solution

Q8. The projection of the line segment joining the points (-1,0,3) and (2,5,1) on the line whose direction ratios are 6,2,3 is:

•  10/7
•  22/7
•  18/7
•  None of these

Solution

Q9. The equation of a line of intersection of planes 4x+4y-5z=12 and 8x+12y-13z=32 can be written as:

•  $$\(\frac{(x-1)}{2}=\frac{(y+2)}{-3}=\frac{z}{4}\)
•  $$\(\frac{(x-1)}{2}=\frac{(y-2)}{3}=\frac{z}{4}\)
•  $$\(\frac{x}{2}=\frac{(y+1)}{3}=\frac{(z-2)}{4}\)$$
•  $$\(\frac{x}{2}=\frac{y}{3}=\frac{(z-2)}{4}\)

Solution

Q10. Let a plane passes through the point P(-1,-1,1) and also passes through a line joining the points Q(0,1,1)Q(0,1,1)and R(0,0,2). Then the distance of the plane from the point (0, 0, 0) is:

•  3
•  0
•  1/√6
• 2/√6

Solution