Advertisements
Advertisements
प्रश्न
A point R with x-coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by `((8k + 2)/(k+1), (-3)/(k+1), (10k + 4)/(k+1))`
Advertisements
उत्तर
The coordinates of points P and Q are given as P (2, –3, 4) and Q (8, 0, 10).
Let R divide line segment PQ in the ratio k:1.
Hence, by section formula, the coordinates of point R are given by
संबंधित प्रश्न
A point is on the x-axis. What are its y-coordinates and z-coordinates?
A point is in the XZ-plane. What can you say about its y-coordinate?
The coordinates of points in the XY-plane are of the form _______.
Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).
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 PA2 + PB2 = k2, where k is a constant.
The mid-points of the sides of a triangle ABC are given by (–2, 3, 5), (4, –1, 7) and (6, 5, 3). Find the coordinates of A, B and C.
A(1, 2, 3), B(0, 4, 1), C(–1, –1, –3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle ∠BAC meets BC.
Find the coordinates of the points which tisect the line segment joining the points P(4, 2, –6) and Q(10, –16, 6).
Using section formula, show that he points A(2, –3, 4), B(–1, 2, 1) and C(0, 1/3, 2) are collinear.
Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, –8) is divided by the yz-plane.
If a parallelopiped is formed by the planes drawn through the points (2,3,5) and (5, 9, 7) parallel to the coordinate planes, then write the lengths of edges of the parallelopiped and length of the diagonal.
If the origin is the centroid of a triangle ABC having vertices A(a, 1, 3), B(−2, b −5) and C (4, 7, c), find the values of a, b, c.
P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.
The equations of x-axis in space are ______.
The points (1, 2, 3), (–2, 3, 4) and (7, 0, 1) are collinear.
Find the position vector of a point A in space such that `vec(OA)` is inclined at 60º to OX and at 45° to OY and `|vec(OA)|` = 10 units
Find the vector equation of the line which is parallel to the vector `3hati - 2hatj + 6hatk` and which passes through the point (1 ,–2, 3).
Show that the lines `(x - 1)/2 = (y - 2)/3 = (z - 3)/4` and `(x - 4)/5 = (y - 1)/2` = z intersect.. Also, find their point of intersection.
The reflection of the point (α, β, γ) in the xy-plane is ______.
A plane passes through the points (2, 0, 0) (0, 3, 0) and (0, 0, 4). The equation of plane is ______.
The equation of a line, which is parallel to `2hati + hatj + 3hatk` and which passes through the point (5, –2, 4), is `(x - 5)/2 = (y + 2)/(-1) = (z - 4)/3`.
