Advertisements
Advertisements
Question
If a line makes angle 90°, 60° and 30° with the positive direction of X, Y and Z axes respectively, find its direction cosines
Solution
Let the direction cosines of the line be l, m, n.
∴ l = cos 90°, m = cos 60°, n = cos 30°
∴ l = 0, m = `1/2`, n = `sqrt(3)/2`
APPEARS IN
RELATED QUESTIONS
The vector equation of the plane r = `(2hat"i" + hat"k") + lambda(hat"i") + mu(hat"i" + 2hat"j" - 3hat"k")` in scalar product form is `"r"*(3hat"i" + 2hat"k") = alpha`, then α = ______.
A point P (x, y, z) lies on the line joining points A (1, 2, 3) and B (2, 10, 1). If x co-ordinates of the point P is -1, then ______
The angle between the planes and `bar"r"*(2hat"i" + hat"j" - hat"k") = 3` and `bar"r"*(hat"i" + 2hat"j" + hat"k") = 1` is ______.
If `|bar"a"| = |bar"b"| = 1, bar"a"*bar"b" = 0` and `bar"a" + bar"b" + bar"c" = bar"0"`, then `|bar"c"|` is equal to ______.
The angle between the line `bar"r" = (hat"i" + 2hat"j" + hat"k") + lambda(hat"i" + hat"j" + hat"k")` and the plane `bar"r"*(2hat"i" - hat"j" + hat"k")` = 8 is ______.
If a line lies in the octant OXYZ and it makes equal angles with the axes, then ______.
The value of `hati . (hatj xx hatk) + hatj . (hatk xx hati) + hatk . (hati xx hatj)` is ______
If `vec"a", vec"b", vec"c"` are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then `[(vec"a" + vec"b" + vec"c", vec"b" - vec"a", vec"c")]` = ______.
The coordinates of the foot of perpendicular from (2, –1, 5) to the line `(x - 11)/10 = (y + 2)/(-4) = (z + 8)/(-11)` are ______.
Using vectors prove that the altitudes of a triangle are concurrent.
The equation of line passing through (3, –1, 2 ) and perpendicular to the lines
`vecr = (hati + hatj - hatk) + λ(2hati - 2hatj + hatk)` and
`vecr = (2hati + hatj - 3hatk) + μ(hati - 2hatj + 2hatk)` is:
If vector r with dc's l, m, n is equally inclined to the coordinate axes, then the total number of such vectors is ______.
Direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are ______.
What will be projection of the vector `4hati - 3hatj + hatk` on the line joining the points (2, 3, – 1) and (– 2, – 4, 3)?
Determine whether `bara " and" barb` are orthogonal, parallel or neither.
`bara=-3/5hati +1/2hatj +1/3hatk, barb= 5hati+4hatj+3hatk `
Determine whether `bara and bar b` are orthogonal, parallel or neither.
`bar"a" = -3/5hat"i" + 1/2hat"j" + 1/3hat"k" , barb = 5hat"i" + 4hat"j" + 3hat"k"`
If a vector has direction angles 45º and 60º find the third direction angle.
If `|bara| = |barb|` = 1 and `|bara + barb| = sqrt(3)`, then the value of `(3bara - 4barb)*(2bara + 5barb)` = ______.
If `bara + barb = barc, |bara| = sqrt(5), |barb| = sqrt(2), |barc|` = 3, then the angle between `barb` and `barc` is ______.
If `|bara + barb| = |bara - barb|, bara` and `barb` are non-zero vectors, find the angle between `bara` and `barb`.
If a vector has direction angles 45° and 60° find the third direction angle.
Find the angle between the line `bar r = (hat i + 2hat j + hat k) + lambda(hat i + hat j + hat k)` and the plane `bar r *(2hat i + hat j + hat k) = 8`.
Find two unit vectors each of which is perpendicular to both `baru` and `barv`, where `baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`
Determine whether `bb(bara)` and `bb(barb)` are orthogonal, parallel, or neither.
`bara = -3/5 hati + 1/2 hatj +1/3 hatk, barb = 5 hati + 4 hatj + 3 hatk`
If a vector has direction angles 45° and 60° find the third direction angle.
If a vector has direction angles 45º and 60º, find the third direction angle.
If a vector has direction angles 45º and 60º find the third direction angle.
If a vector has direction angles 45ºand 60º find the third direction angle.
Determine whether `bara and barb` are orthogonal, parallel or neither.
`bara = -3/5hati + 1/2 hatj + 1/3hatk, barb = 5 hati + 4hatj + 3hatk`
If a vector has direction angles 45° and 60° find the third direction angle.
Find two unit vectors each of which is perpendicular to both `baru` and `barv`, where `baru = 2hati + hatj - 2hatk, barv = hati + 2hatj - 2hatk`.
