91.Find the co-ordinates of a point B which divides the line joining O (0, 0, 0) and A (4, - 1, -2) externally in ratio 1 : 2 Show also that O is the mid-point of AB.
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92.Find the co-ordinates of a point R which divides the join of P ((x1,y1,z1) and Q (x2, y2, z2) externally in the ratio 1 : 2. Verify that P is mid-point of QR.
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Short Answer Type
93.Find the co-ordinates of the points which trisect the line segment joining the points P (4, 2, -6) and Q (10, -16, 6).
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94.If G (1, -1, 2) is the centroid of a triangle ABC whose vertices are A (x, 0, 1), B (-2, y, - 5) and C (1, 6, z). Find the values of x, y and z.
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95.The vertices of a triangle ABC are A (5,4, 6), B (1, -1, 3) and C (4, 3, 2). The internal bisector of ∠ A meets BC in D. Find (i) the co-ordinates of point D (ii) the length AD.
96.Prove that A (1, 3 0), B (-5, 5, 2) C (-9, - 1, 2) and D (-3, -3, 0) taken in order, form the vertices of a parallelogram. Do they form a rectangle also ?
Solution not provided. Ans. No
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97.A (3, -1, -1), B (5, - 4, 0) and C (2, 3, -2) are three vertices of a parallelogram ABCD. Find the co-ordinates of the fourth vertex D.
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98.A (2, 6, -4) and B (4, -2, 3) are two vertices of a triangle ABC whose centroid is G (7, - 2, 5). Find the co-ordinates of the third vertex C.
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99.
Using section formula, show that points A (2, -3, 4), B (-1, 2, 1) and are collinear.
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100.Using section formula, show that points A (3, 2, -4), B (5, 4, -6) and C (9, 8, -10) are collinear. Find the ratio in which point C divides AB.
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are collinear.
