introduction to three dimensional geometry

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Asked: August 25, 2020In: NCERT 11th Maths

6. If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that $PA^2 + PB^2 = k^2$ , where k is a constant.

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Asked: August 25, 2020In: NCERT 11th Maths

5. A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.

eduhilfe

Asked: August 25, 2020In: NCERT 11th Maths

4. Find the coordinates of a point on y-axis which are at a distance of $5\sqrt{ 2}$ from the point P (3, –2, 5).

eduhilfe

Asked: August 25, 2020In: NCERT 11th Maths

3. If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.

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Asked: August 25, 2020In: NCERT 11th Maths

2. Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).

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Asked: August 25, 2020In: NCERT 11th Maths

1. Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

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Asked: August 25, 2020In: NCERT 11th Maths

5. Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6).

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Asked: August 25, 2020In: NCERT 11th Maths

4. Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and C $(0,\frac{1}{3},2)$ are collinear.

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Asked: August 25, 2020In: NCERT 11th Maths

3. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

eduhilfe

Asked: August 25, 2020In: NCERT 11th Maths

2. Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR

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6. If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that $PA^2 + PB^2 = k^2$ , where k is a constant.

5. A point R with x-coordinate 4 lies on the line segment joining the points P(2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.

4. Find the coordinates of a point on y-axis which are at a distance of $5\sqrt{ 2}$ from the point P (3, –2, 5).

3. If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.

2. Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).

1. Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

5. Find the coordinates of the points which trisect the line segment joining the points P (4, 2, – 6) and Q (10, –16, 6).

4. Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and C $(0,\frac{1}{3},2)$ are collinear.

3. Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

2. Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR

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