Advertisements
Advertisements
Question
Planes are drawn parallel to the coordinate planes through the points (3, 0, –1) and (–2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.
Advertisements
Solution
Let P\[\equiv\](3, 0, −1), Q\[\equiv\](−2, 5, 4)
PE = Distance between the parallel planes ABCP and FQDE
=\[\left| 4 + 1 \right| = 5\]
(These planes are perpendicular to the z-axis)
PA = Distance between the parallel planes ABQF and PCDE
= \[\left| - 2 - 3 \right| = 5\]
(These planes are perpendicular to the x-axis)
Similarly, PC =\[\left| 5 - 0 \right| = 5\]
Thus, the length of the edges of the parallelepiped are 5, 5 and 5
APPEARS IN
RELATED QUESTIONS
Name the octants in which the following points lie:
(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5),
(–3, –1, 6), (2, –4, –7).
The x-axis and y-axis taken together determine a plane known as_______.
Coordinate planes divide the space into ______ octants.
Name the octants in which the following points lie:
(7, 4, –3)
Name the octants in which the following points lie:
(–5, –3, –2)
Find the image of:
(–5, 4, –3) in the xz-plane.
Find the distances of the point P(–4, 3, 5) from the coordinate axes.
Determine the points in zx-plane are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).
Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).
If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.
Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle.
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle.
Verify the following:
(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.
Find the locus of the point, the sum of whose distances from the points A(4, 0, 0) and B(–4, 0, 0) is equal to 10.
Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.
Write the distance of the point P (2, 3,5) from the xy-plane.
Find the point on x-axis which is equidistant from the points A (3, 2, 2) and B (5, 5, 4).
The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is
Let (3, 4, –1) and (–1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to
What is the locus of a point for which y = 0, z = 0?
Find the co-ordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
If a line makes an angle of `pi/4` with each of y and z axis, then the angle which it makes with x-axis is ______.
Find the equation of the plane through the points (2, 1, 0), (3, –2, –2) and (3, 1, 7).
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
Find the angle between the lines whose direction cosines are given by the equations l + m + n = 0, l2 + m2 – n2 = 0
If a variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn2
Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.
Find the equations of the line passing through the point (3,0,1) and parallel to the planes x + 2y = 0 and 3y – z = 0.
Find the equation of the plane through the points (2, 1, –1) and (–1, 3, 4), and perpendicular to the plane x – 2y + 4z = 10.
Show that the straight lines whose direction cosines are given by 2l + 2m – n = 0 and mn + nl + lm = 0 are at right angles.
If l1, m1, n1 ; l2, m2, n2 ; l3, m3, n3 are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l1 + l2 + l3, m1 + m2 + m3, n1 + n2 + n3 makes equal angles with them.
If the directions cosines of a line are k, k, k, then ______.
The sine of the angle between the straight line `(x - 2)/3 = (y - 3)/4 = (z - 4)/5` and the plane 2x – 2y + z = 5 is ______.
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.
The locus represented by xy + yz = 0 is ______.
The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is ______.
The cartesian equation of the plane `vecr * (hati + hatj - hatk)` is ______.
