Advertisements
Advertisements
प्रश्न
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Advertisements
उत्तर
The given direction ratios are a = 3, b = – 1 , c = 3
If a, b, c are the direction ratios of a vector ten the direction cosines of the vector are
l = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
m = `"b"/sqrt("a"^2 + "b"^2 + "c")`
c = `"c"/sqrt("a"^2 + "b"^2 + "c")`
∴ The required direction cosioes of the water are
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`(-1)/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(9 + 1 + 9)`
`(- 1)/sqrt(9 + 1 + 9)`
`3/sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1)/sqrt(9 + 1+ 9))`
`3/sqrt(9 + 1 + 9)`
`1/sqrt(19), (-1)/sqrt(19)`
= `3sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1) /sqrt(19), 3/sqrt(19))`
APPEARS IN
संबंधित प्रश्न
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.
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).
What are the direction cosines of Z-axis?
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
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 angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.
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
The angle between the two diagonals of a cube is
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.
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
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 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
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
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.
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 ______.
