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Home > Sequences And Series

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Sequences And Series

Question
CBSEENMA11014982
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Find points on x - axis which are at a distance of square root of 29 units from point A (1, 2, 3).

Solution
Short Answer

Let the required point on x-axis be P (x, 0, 0)
It is at a distance of square root of 29 units from A (1, 2, 3)
rightwards double arrow                             open vertical bar PA close vertical bar space equals space square root of 29 space rightwards double arrow space square root of left parenthesis straight x minus 1 right parenthesis squared plus left parenthesis 0 minus 2 right parenthesis squared plus left parenthesis 0 minus 3 right parenthesis squared end root space equals space square root of 29
rightwards double arrow                 straight x squared minus 2 straight x plus 14 space equals space 29 space rightwards double arrow space space space straight x squared minus 2 straight x minus 15 equals 0
rightwards double arrow                space space space left parenthesis straight x minus 5 right parenthesis space left parenthesis straight x plus 3 right parenthesis space equals space 0 space rightwards double arrow space straight x equals 5 comma space straight x equals negative 3
Hence, the required points on x-axis are (5, 0, 0) or (-3, 0, 0).


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Some More Questions From Sequences and Series Chapter

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.

Find the octant in which the following points lie:
A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).

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