Question

Find the locus of a point P (x, y, z), where x > y > z > 0, such that its distance from ZX-plane exceeds ¹/₂ the sum of its distances from XY-plane and YZ-plane by 2.

Solution

The point is P(x, y, z), where x, y, z>0
Distance from ZX-plane = $space space open vertical bar straight y close vertical bar space equals space straight y$
Distance from XY-plane = $open vertical bar straight z close vertical bar equals straight z$
Distance from YZ-plane = $open vertical bar straight x close vertical bar equals straight x$
According to the question, we have
$space space space space space space space space space straight y minus 1 half left parenthesis straight z plus straight x right parenthesis equals 2$
$rightwards double arrow$ 2y - z - x = 4
Hence, the locus is x - 2y + z + 4 =0

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 locus of a point P (x, y, z), where x > y > z > 0, such that its distance from ZX-plane exceeds ¹/₂ the sum of its distances from XY-plane and YZ-plane by 2.

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

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Sequences And Series

Find the locus of a point P (x, y, z), where x > y > z > 0, such that its distance from ZX-plane exceeds 1/2 the sum of its distances from XY-plane and YZ-plane by 2.

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

Find the locus of a point P (x, y, z), where x > y > z > 0, such that its distance from ZX-plane exceeds ¹/₂ the sum of its distances from XY-plane and YZ-plane by 2.

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).