Advertisements
Advertisements
Question
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
Advertisements
Solution
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
RELATED QUESTIONS
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
Show that the line through points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (−1, −2, 1) and (1, 2, 5).
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 angle between the lines whose direction cosines are given by the equations
(i) l + m + n = 0 and l2 + m2 − n2 = 0
What are the direction cosines of X-axis?
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
If a unit vector `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with } \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
The angle between the two diagonals of a cube is
If a line makes angles α, β, γ, δ with four diagonals of a cube, then cos2 α + cos2 β + cos2γ + cos2 δ is equal to
Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines
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
`3hat"i" + hat"j" + hat"k"`
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
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 co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are ______.
If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l2 + m2 + cnl = 0 are parallel, then the positive value of c is ______.
Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.
