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Sequences And Series

Question
CBSEENMA11015010
Wired Faculty App

Find the co-ordinates of the point which divides the line segment formed by joining the points (- 2, 3, 5) and (1, -4, 6) in the ratio of 2 : 3  externally.

Solution

The ratio is 2 : 3 externally.
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          space space straight y equals fraction numerator 2 space left parenthesis negative 4 right parenthesis plus left parenthesis negative 3 right parenthesis space left parenthesis 3 right parenthesis over denominator 2 plus left parenthesis negative 3 right parenthesis end fraction equals fraction numerator negative 8 minus 9 over denominator negative 1 end fraction equals 17
                                                                         
                 straight z equals fraction numerator 2 left parenthesis 6 right parenthesis plus left parenthesis negative 3 right parenthesis left parenthesis 5 right parenthesis over denominator 2 plus left parenthesis negative 3 right parenthesis end fraction equals fraction numerator 12 minus 15 over denominator negative 1 end fraction equals 3
∴ Point Q is (-8, 17, 3)

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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