Advertisements
Advertisements
प्रश्न
A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is
पर्याय
2
3
4
all of these
Advertisements
उत्तर
all of these
The given points (5, 7, 9) and (2, 3, 7) are two diagonally opposite vertices of the parallelopiped as all of their coordinates are different
∴ Edges of the parallelopiped = |5−2|, |7−3|, |9−7| =3, 4, 2
APPEARS IN
संबंधित प्रश्न
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1.
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.
Define direction cosines of a directed line.
Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).
A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
Write the distance of the point P (x, y, z) from XOY plane.
Find the distance of the point (2, 3, 4) from the x-axis.
Write direction cosines of a line parallel to z-axis.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
For every point P (x, y, z) on the x-axis (except the origin),
Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line `vec("r") = (-2hat"i"+3hat"j") +lambda(2hat"i"-3hat"j"+6hat"k").`Also, find the distance between these two lines.
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.
If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.
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.
If the directions cosines of a line are k,k,k, then ______.
The line `vec"r" = 2hat"i" - 3hat"j" - hat"k" + lambda(hat"i" - hat"j" + 2hat"k")` lies in the plane `vec"r".(3hat"i" + hat"j" - hat"k") + 2` = 0.
If a line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.
Find the direction cosine of a line which makes equal angle with coordinate axes.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
