Tag: coordinates in 3d

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Questions Related to coordinates in 3d

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

The coordinates of any point, which lies on $x$ axis are

  1. $(0,x,0)$

  2. $(x,0,0)$

  3. $(x,x,0)$

  4. $(x,x,x)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 3-dimensional plane, the point which lies on $x$-axis does not have any part in y and z axes.

At that point, the value of $y$ and $z$ will be $0$.
Hence, coordinate of any point which lies on $x$ axis are $(x,0,0)$.

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

A point at which all the three perpendicular coordinate axes meets is known as 

  1. Meeting point

  2. Origin

  3. Triple point

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The three perpendicular coordinate axes meets at one of the point which divides the plane into eight quadrant.

The $1^{st}$ quadrant has all positive points, $2^{nd}$ has $x$ -ve and remaining $2$ +ve points and so on.
Only $(0,0,0)$ is not included in any quadrant and is the intersection point.
Thus, the three axes meet at $(0,0,0)$ from where the eight quadrants originate.
Hence, the point is known as origin.

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

If point $p$ lies in first octant, then the sign of $x-$ coordinate will always be 

  1. $+$

  2. $-$

  3. $x$ coordinate is always $0$

  4. $x$ coordinate can be $+$ or $-$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In the first octant, the values of x,y and z axes are positive.

Any point which lies in first octant has all their coordinate values as positive.
Since point $p$ lies in first octant, so, p will have all its coordinates as positive.
Hence, sign of $x$-coordinate will always be $+$.

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

Examine if the following is true statement.
The cube can cast a shadow in the shape of a rectangle.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formation of shadow is equivalent to cutting of cube . We know that cutting cube always gives a square or a rectangle . so, it can cast a shadow of a rectangle.

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

Examine if the following is true statement.
The cube can cast a shadow in the shape of a hexagon.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
False
The cube cannot cast shadow in shape of hexaxon because of following reason:
no matter whatever the position of light source focussing on cube it always cast a shadow of either square or rectangle .
Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

State the following statement is True or False
Two distinct lines intersecting each other in a plane can have two points in common

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Answer is option B (False)
Two distinct lines intersecting each other  in a plane cannot have more than one point in common

Multiple choice maths introduction to three dimensional geometry coordinate axes and coordinate planes in 3d space coordinates in 3d introduction to 3d geometry

State the following statement is True or False
If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
suppose lines $l1$ and $l2$ intersect at two disticnt points say P and Q.Then $l1$ contains points P and Q.
Also, $l2$ contains points P and Q.
So two lines $l1$ and $l2$ pass through two distinct points P and Q.
But only one line can pass through two different points.  (axiom 3)
Hence, two lines cannot have more than one point in common.
$\therefore$ Option A  is correct.