Coordinate Planes in Three Dimensional Space

Q.

How do you find the general form of an equation?

Q. Find the area of the region bounded by curves $y^2=9x,y=3x$

Q.

X and Y coordinates of point on XY plane are Zero - True or False?

1. True

2. False

Q. Find the area of circle $4x^2+4y^2=9$ which is interior to the parabola $x^2=4y$.

Q.

If a and b are the position vectors of two points A and B and C is a point on AB produced such that AC = 3AB, then position vector of C will be

1. 3b - 2a

2. 3a - 2b

3. 3b - a

4. 3a - b

Q. Among the following points, the one lying on the XY plane is .

1. (0, 0, 1)
2. (1, 1, 0)
3. (0, 1, 1)
4. (1, 0, 1)

Q. If the lines $2x-3y=5$ and $3x-4y=7$ are diameters of a circle of area $154$ square units, then obtain the equation of the circle.

Q.

Which of the following points lie on XZ plane?

1. (1, 0, 1)

2. (1, 1, 0)

3. (1, 2, 3)

4. (0, 2, 3)

Q. Find the area of the region
$\left\{\right(x,y):0\le y\le x^2+1,0\le y\le x+1,0\le x\le 2\}$

Q. How to find image of a point P(1, 3, 2) w.r.t a plane 2x-y+z = 2 ?

Q.

X and Y coordinates of point on XY plane are Zero

1. True

2. False

Q. Let $[.]$ denote the greatest integer function. The area (in sq. units) bounded by the curves $y=[\frac{x^2}{64}+2],$ $y=x-1,$ $x=0$ above the $x-$axis is

Q. For every point P (x, y, z) on the xy-plane,
(a) x = 0
(b) y = 0
(c) z = 0
(d) x = y = z = 0

Q. 33. Planes are drawn parallel to the coordinate planes through the points(1, 2, 3) and (3, -4, -5).The length of the edges of the parallelopiped so formed is given by ?

Q. If and denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.

Q. $(-1,-5,-7)$ lies in Octant

1. I
2. V
3. III
4. VII

Q.

X and Y coordinates of point on XY plane are Zero

1. True

2. False

Q.

X and Y coordinates of point on XY plane are Zero

1. True

2. False

Q.

In a three dimensional space the equation $x^2-5x+6=0$ represents

1. points

2. curves

3. pair of straight lines

4. planes

Q.

X and Y coordinates of point on XY plane are Zero

1. False

2. True

Q. $\text{Select the points which lie in the first octant:}$

1. (1, 2, 3)
2. (-2, 3, 7)
3. (5, 9, -6)
4. (5, 6, 8)
5. (8, 3, 4)
6. (-1, -5, -6)
7. (1, 1, -1)
8. (2, 2, 2)
9. (99, 8, 5)

Q. In which plane does the point $(4,-3,0)$ lie?

Q. What is the distance of the point ( 0 , -3 ) from origin?

Q.

Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).

Q. The number of octants in which $Z$ coordinate is positive is

1. $2$
2. $3$
3. $4$
4. $1$

Q. $\text{Select the points which lie in the first octant:}$

1. (1, 2, 3)
2. (-2, 3, 7)
3. (5, 9, -6)
4. (5, 6, 8)
5. (8, 3, 4)
6. (-1, -5, -6)
7. (1, 1, -1)
8. (2, 2, 2)
9. (99, 8, 5)

Q. 20 If A=(0, 4, -3) and B=(1, 2, -2) be any two points , then the point which lies on the angle bisector of OA and OB IS (O is the origin