Advertisements
Advertisements
Question
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Advertisements
Solution
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
RELATED QUESTIONS
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 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.
What are the direction cosines of Z-axis?
Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.
A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is
The distance of the point P (a, b, c) from the x-axis is
Verify whether the following ratios are direction cosines of some vector or not
`1/sqrt(2), 1/2, 1/2`
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
`5hat"i" - 3hat"j" - 48hat"k"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is
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 ______.
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.
A line in the 3-dimensional space makes an angle θ `(0 < θ ≤ π/2)` with both the x and y axes. Then the set of all values of θ is the interval ______.
Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?
A line passes through \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\]. Which is one set of direction ratios of the line?
