Advertisements
Advertisements
प्रश्न
Verify whether the following ratios are direction cosines of some vector or not
`1/sqrt(2), 1/2, 1/2`
Advertisements
उत्तर
The given ratios are l = `1/sqrt(2)`, m = `1/2`, n = `1/2`
l2 + m2 + n2 = `(1/sqrt(2))^2 + (1/2)^2 + (1/2)^2`
= `1/2 + 1/4 + 1/4`
= `1/2 + 1/2`
= 1
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
∴ The given ratio form the direction cosines of a vector.
APPEARS IN
संबंधित प्रश्न
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
What are the direction cosines of X-axis?
Find the distance of the point (2, 3, 4) from the x-axis.
Write direction cosines of a line parallel to z-axis.
Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c
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 `pi/4` with each of y and z-axis, then the angle which it makes with x-axis 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 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
If the directions cosines of a line are k,k,k, then ______.
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
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`.
