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Introduction to Three Dimensional Geometry Test - 10

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Introduction to Three Dimensional Geometry Test - 10
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  • Question 1
    1 / -0
    A point at which all the three perpendicular coordinate axes meets is known as 
    Solution
    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.
  • Question 2
    1 / -0
    The coordinates of any point, which lies on $$x$$ axis are
    Solution
    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 $$(x,0,0)$$.
  • Question 3
    1 / -0
    Point $$D$$ has coordinates as $$(3,4,5)$$. Referring to the given figure, find the coordinates of point $$C$$.

    Solution
    It is given that $$D=(3,4,5)$$. Then, obviously, $$E=(0,4,5)$$. Since the point C lies on y axis, hence the corresponding point C will be (from the coordinates of E we found earlier ) $$C=(0,4,0)$$.
  • Question 4
    1 / -0
    Point $$D$$ has coordinates as $$(3,4,5)$$. Referring to the given figure, find the coordinates of point $$B$$.

    Solution
    From the given figure, D has x-coordinate $$=3$$, y-coordinate $$=4$$ and z-coordinate $$=5$$.
    The point B lies in xy-plane. So, z-coordinate will be $$0$$.
    B is in the same line of point D. 
    $$\therefore$$ x and y coordinates will be same as of point D.
    Hence, coordinates of point B is $$(3,4,0)$$.
  • Question 5
    1 / -0
    Point $$D$$ has coordinates as $$(3,4,5)$$. Find the coordinates of the point $$F$$.

    Solution
    From the given figure, D has x-coordinate $$=3$$, y-coordinate $$=4$$ and z-coordinate $$=5$$.
    Lines GF and DE are parallel and has the same height.
    $$\therefore$$ All four points D,E,F and G has z-coordinate same i.e. $$5$$.
    Point F lie on z-axis $$\implies$$ x-coordinate and y-coordinate are $$0$$.
    Hence, coordinates of F is $$(0,0,5)$$.
  • Question 6
    1 / -0
    The coordinate of any point, which lies in $$xy$$ plane , is
    Solution
    Given that the point lies in $$xy$$ plane
    In $$xy$$ plane , the coordinate of $$z$$ will be zero
    So $$(x,x,0)$$ represents a point which lies in $$xy$$ plane
    Therefore option $$B$$ is correct
  • Question 7
    1 / -0
    Point $$D$$ has coordinates as $$(3,4,5)$$. Find the coordinates of point $$G$$.

    Solution
    From the given figure, D has x-coordinate $$=3$$, y-coordinate $$=4$$ and z-coordinate $$=5$$.
    The points A,B,D and G form a rectangle whose x-coordinate is same i.e. $$3$$.
    So, G has x-coordinate as $$3$$.
    G lie on the same height as D i.e. z-coordinate will be same.
    $$\therefore$$ G has z-coordinate $$=5$$.
    Since, G lie on XZ plane $$\implies y-$$coordinate is $$0$$.
    Hence, coordinates of point G is $$(3,0,5)$$.
  • Question 8
    1 / -0
    In which octant, does $$(-4,2,3)$$ lie?
    Solution
    The three perpendicular coordinate axes meet at one of the points which divide the plane into eight quadrants.

    The $$1^{st}$$ quadrant has all positive points, $$2^{nd}$$ has $$x$$ -ve and remaining $$2$$ are +ve points and so on.

    Thus, the point $$(-4,2,3)$$ lies in $$II$$ octant.

  • Question 9
    1 / -0
    If point $$p$$ lies in first octant, then the sign of $$x-$$ coordinate will always be 
    Solution
    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 $$+$$.
  • Question 10
    1 / -0
    Point $$D$$ has coordinates as $$(3,4,5)$$. Referring to the given figure, find the coordinates of point $$A$$.

    Solution
    From the given figure, D has x-coordinate $$=3$$, y-coordinate $$=4$$ and z-coordinate $$=5$$.
    The points A,B,D and G form a rectangle whose x-coordinate is same i.e. $$3$$.
    Point A lies on x-axis and thus, y and z coordinates will be $$0$$.
    Hence, coordinates of point A is $$(3,0,0)$$.
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