Find the value of x, so that the point (6, 5, -3) is at a distance of 13 units from the point (x, -7, 0).

Solution

The given points are A (6, 5, -3) and B (x, -7, 0)
Given that $space space space open vertical bar AB close vertical bar space equals space 13$
$rightwards double arrow$ $square root of left parenthesis 6 minus straight x right parenthesis squared plus left parenthesis 5 plus 7 right parenthesis squared plus left parenthesis negative 3 minus 0 right parenthesis squared end root space equals space 13$
Squaring both sides, we get
$straight x squared plus 36 minus 12 straight x plus 144 plus 9 equals 169 space rightwards double arrow space straight x squared minus 12 straight x plus 20 equals 0$
$rightwards double arrow$ $space space space left parenthesis straight x space minus 2 right parenthesis space left parenthesis straight x minus 10 right parenthesis space equals space 0$ $rightwards double arrow$ x = 2, x = 10
Hence, the value of x is 2 or 10.

Some More Questions From Sequences and Series Chapter

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

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Sequences And Series

Find the value of x, so that the point (6, 5, -3) is at a distance of 13 units from the point (x, -7, 0).

Some More Questions From Sequences and Series Chapter

The x-axis and y-axis taken together determine a plane known as ____________.

The coordinates of points in the XY-plane are of the form __________.

Coordinate planes divide the space into _______ octants.

Let P (-2, 3, -4) is a point in space. Find the co-ordinates of the foot of perpendicular from this point to ZX-plane.

Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Sequences And Series

Find the value of x, so that the point (6, 5, -3) is at a distance of 13 units from the point (x, -7, 0).

Some More Questions From Sequences and Series Chapter

The x-axis and y-axis taken together determine a plane known as ____________.

The coordinates of points in the XY-plane are of the form __________.

Coordinate planes divide the space into _______ octants.

Let P (-2, 3, -4) is a point in space. Find the co-ordinates of the foot of perpendicular from this point to ZX-plane.

Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

Name the octants in which the following points lie:A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).