Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`3hat"i" + hat"j" + hat"k"`
उत्तर
The direction ratios of the vector `3hat"i" + hat"j" + hat"k"` are (3, 1, 1)
The direction cosines of the vector `3hat"i" + hat"j" + hat"k"` are
`3/sqrt(3^2 + 1^2 + 1^2), 1/sqrt(3^2 + 1^2 + 1^2), 1/sqrt(3^2 + 1^2 + 1^2)`
`3/sqrt(9 + 1 + ), 1/sqrt(9 + 1 + 1), 1/sqrt(9 + 1 + 1)`
`(3/sqrt(11), 1/sqrt(11), 1/sqrt11)`
Direction ratios = (3, 1, 1)
Direction cosines = `(3/sqrt(11), 1/sqrt(11), 1/sqrt11)`
APPEARS IN
संबंधित प्रश्न
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
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).
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?
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
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
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line 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 ______.
O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.
If the directions cosines of a line are k,k,k, then ______.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
