Advertisements
Advertisements
प्रश्न
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
उत्तर
The given ratios are l = `1/5`, m = `3/5`, n = `4/5`
l2 + m2 + n2 = `(1/5)^2 +(3/5)^2 + (4/5)^2`
= `1/25 + 9/25 + 16/25`
= `(1 + 9 + 16)/25`
= `26/25 ≠ 1`
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
∴ The given ratio `1/5, 3/5, 4/5` do not form the direction cosines of a vector.
APPEARS IN
संबंधित प्रश्न
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
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).
If the coordinates of the points A, B, C, D are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2), then find the angle between AB and CD.
Find the angle between the lines whose direction cosines are given by the equations
(i) l + m + n = 0 and l2 + m2 − n2 = 0
Find the angle between the lines whose direction cosines are given by the equations
l + 2m + 3n = 0 and 3lm − 4ln + mn = 0
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
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 direction cosines of a vector whose direction ratios are
1, 2, 3
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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 line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ 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 ______.
The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`
Find the direction cosine of a line which makes equal angle with coordinate axes.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
