Advertisements
Advertisements
प्रश्न
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
Advertisements
उत्तर
The given direction ratios are a = 0, b = 0, c = 7
If a, b, c are the direction ratios of a vector then the direction cosines of the vector are
l = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
m = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
c = `"c"/sqrt("a"^2 + "b"^2 + "c"^2)`
∴ The required direction cosines of the water are
= `0/sqrt(0^2 + 0^2 + 7), 0/sqrt(0^2 + 0^2 + 7^2), 7/sqrt(0^2 + 0^2 + 7^2)`
= `0/7, 0/7, 7/7`
= (0, 0, 1)
APPEARS IN
संबंधित प्रश्न
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.
Find the direction cosines of a line which makes equal angles with the coordinate axes.
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the distance of the point (3, −5, 12) from X-axis?
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.
Find the distance of the point (2, 3, 4) from the x-axis.
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.
If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.
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 a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
