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Sequences And Series

Question
CBSEENMA11015642
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If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

  • G.P.

  • A.P.

  • Arithmetic − Geometric Progression

  • H.P.

Solution

B.

A.P.

increment space equals space 1 half straight p subscript 1 straight a space equals space 1 half straight p subscript 2 straight b space equals space 1 half straight p subscript 3 straight b straight p subscript 1 comma space straight p subscript 2 comma space straight p subscript 3 space are space in space straight H. straight P. rightwards double arrow space fraction numerator 2 increment over denominator straight a end fraction comma fraction numerator 2 increment over denominator straight b end fraction comma fraction numerator 2 increment over denominator straight c end fraction space are space in space straight H. straight P. rightwards double arrow space 1 over straight a comma 1 over straight b comma 1 over straight c space are space in space straight H. straight P rightwards double arrow straight a comma straight b comma space straight c space are space in space straight A. straight P rightwards double arrow space sin space straight A comma space sin space straight B comma space sin space straight C space are space in space straight A. straight P.

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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