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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
<br
*** QuickLaTeX cannot compile formula: *** Error message: Error: Nothing to show, formula is empty
length of the side of the square is
unit.