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If \( A(1,2,3), \quad B (0, 4,2) \text { and } C (x,y,z) \) are three points on a line, where \( A \) divides \( \overline{BC} \) in ratio \( 1:2 \) externally, then find the coordinates of \( C \).
, divides in ratio externally i.e., , divides in ratio internally, i.e., is the midpoint of .
If \(A (1,6,7), B (x,y,z) \text { and } C (3,4,5) \) are three points on a line. If \( C \) divides \( \overline{AB} \) in \( 2:1 \) ratio externally, then find the coordinate of \( B \).
divides in ratio externally.
If \( B(2,3,4) \) be the midpoint of \( A(1,a,3) \text { and } C (b, 4,5) \), line joining \( \overline{AC} \), then find \( a \) and \( b \).
If \(G \left( 1,4, \dfrac{1}{3} \right) \) divides the line joining \( A (x,y,z) \text { and } B(1,5,1) \) in ratio internally, then find the coordinate of \( A \).
A ball is a solid region in the space enclosed by a _____
A ball is a solid hollow sphere.
The planes \( x=a, \quad y=b\) represents______
, represents the plane parallel to plane.
, represents the plane parallel to plane.
So, the intersection of is the line parallel to axis.
The planes \( x=a, \quad z=c\) represents the line_________
, represents the plane parallel to plane.
, represents the plane parallel to plane.
So, the intersection of is the line parallel to axis.
The planes \( y=b, \quad z=c \) represents the line_______
, represents the plane parallel to plane.
, represents the plane parallel to plane.
So, the intersection of is the line parallel to axis.
In a rhombus \( A (5, 9, 3) \text { and } C(3, 5,7) \) are the endpoints on the diagonal \(\overline{AC} \). Find the intersecting point of two diagonals \( \overline{AC} \text { and } \overline{BD} \).
Let be the intersection of .
Hence
If the distance between the points \((5,7,a) \text { and } (3,9,4) \) is \( 3 \), then find \( a \).
If \( A(5,7,3) \text { and } B (3,9,1) \) are the coordinates of the two endpoints of a diameter of a circle, then find the coordinate of the centre.
Let be the centre of the circle.
Let \(A (7,8,9) \text { and } B (9,2,1) \) are two points on a circle with centre \( O (1,5,5) \), then \( \overline{AB} \) is divided by \( O \) in ratio_____
‘ ‘ divides in ratio .
If a point \( P \) lies in \( yz \)plane, then the coordinates of a point ‘\(P \)’ on \(yz \)plane are of the form________
On plane, .
So, the coordinates of the required point is
If a point \( P \) lies in \( xy \)plane, then the coordinates of the point \(P \) on \(xy \)plane are of the form_____
On plane, .
So, the coordinates of the required point is
If a point \( P \) lies on \( zx \)plane, then the coordinates of point \( P \) on \( zx \)plane are of the form______
On plane,
So, the coordinates of the required point is
If a line is parallel to \( x\)axis then , it is ________
axis is perpendicular to plane.
So, any line parallel to axis is perpendicular to plane.
If a liine is parallel to \(y \)axis, then it is________
axis is perpendicular to plane.
So, any line parallel to axis is perpendicular to plane.
If a line is parallel to \( z\)axis then , it is ________
axis is perpendicular to plane.
So, any line parallel to axis is perpendicular to plane.
If a line is parallel to \( x \)axis, then which of the following is false?
axis is perpendicular to axis, axis and plane. So, any line parallel to axis is not parallel to plane.
If a line is parallel to \(y \)axis, then which of the following is false?
axis is perpendicular to axis, axis and plane. So,any line parallel to axis is not parallel to plane.
If a line is parallel to \(z \)axis then which of the following is false?
axis is perpendicular to axis, axis and plane.
So, any line parallel to axis is not parallel to plane.
If a line is perpendicular to \(yz \)plane, then which of the following is false?
Option 2 is false because any line perpendicular to plane is parallel to axis.
If a line is perpendicular to \(zx \)plane, then which of the following is false?
Any line perpendicular to plane is parallel to axis.
Hence, Option 1 is incorrect.
If a line is perpendicular to \( xy \)plane then which of the following is false?
Any line perpendicular to plane is parallel to axis.
Hence, Option 4 is false.
If the end points of a diagonal of a square are \( (1,2,3) \text { and } (2,3,5) \), then the length of the side of the square is_______
Let
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length of the side of the square is unit.