Advertisements
Advertisements
Question
Find the distance between the points P and Q having coordinates (–2, 3, 1) and (2, 1, 2).
Solution
PQ = \[\sqrt{\left( x_2 - x_1 \right)^2 + \left( y_2 - y_1 \right)^2 + \left( z_2 - z_1 \right)^2}\]
\[= \sqrt{\left( 2 + 2 \right)^2 + \left( 1 - 3 \right)^2 + \left( 2 - 1 \right)^2}\]
\[ = \sqrt{\left( 4 \right)^2 + \left( - 2 \right)^2 + \left( 1 \right)^2}\]
\[ = \sqrt{16 + 4 + 1}\]
\[ = \sqrt{21} \text{ units }\]
APPEARS IN
RELATED QUESTIONS
Find the distance between the pairs of points:
(2, 3, 5) and (4, 3, 1)
Find the distance between the following pairs of points:
(–3, 7, 2) and (2, 4, –1)
Find the distance between the following pairs of points:
(–1, 3, –4) and (1, –3, 4)
Find the distance between the following pairs of points:
(2, –1, 3) and (–2, 1, 3)
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.
Verify the following:
(0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right angled triangle.
Verify the following:
(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.
Find the distance between the following pairs of points:
P(1, –1, 0) and Q(2, 1, 2)
Find the distance between the following pairs of point:
A(3, 2, –1) and B(–1, –1, –1).
Using distance formula prove that the following points are collinear:
P(0, 7, –7), Q(1, 4, –5) and R(–1, 10, –9)
Determine the points in yz-plane and are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).
Show that the points A(1, 3, 4), B(–1, 6, 10), C(–7, 4, 7) and D(–5, 1, 1) are the vertices of a rhombus.
Show that the points (3, 2, 2), (–1, 4, 2), (0, 5, 6), (2, 1, 2) lie on a sphere whose centre is (1, 3, 4). Find also its radius.
Find the centroid of a triangle, mid-points of whose sides are (1, 2, –3), (3, 0, 1) and (–1, 1, –4).
If the distance between the points P(a, 2, 1) and Q (1, −1, 1) is 5 units, find the value of a.
Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, −5, 7) and (3, 0, 1).
Find the distance of the point whose position vector is `(2hati + hatj - hatk)` from the plane `vecr * (hati - 2hatj + 4hatk)` = 9
Find the distance of the point (–1, –5, – 10) from the point of intersection of the line `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5.
The distance of a point P(a, b, c) from x-axis is ______.
Prove that the line through A(0, –1, –1) and B(4, 5, 1) intersects the line through C(3, 9, 4) and D(– 4, 4, 4).
Find the equation of a plane which is at a distance `3sqrt(3)` units from origin and the normal to which is equally inclined to coordinate axis
Find the shortest distance between the lines given by `vecr = (8 + 3lambdahati - (9 + 16lambda)hatj + (10 + 7lambda)hatk` and `vecr = 15hati + 29hatj + 5hatk + mu(3hati + 8hatj - 5hatk)`
Find the equation of the plane through the intersection of the planes `vecr * (hati + 3hatj) - 6` = 0 and `vecr * (3hati + hatj + 4hatk)` = 0, whose perpendicular distance from origin is unity.
Distance of the point (α, β, γ) from y-axis is ______.
The distance of the plane `vecr * (2/4 hati + 3/7 hatj - 6/7hatk)` = 1 from the origin is ______.
