Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`3hat"i" + hat"j" + hat"k"`
Advertisements
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
Find the direction cosines of the line
`(x+2)/2=(2y-5)/3; z=-1`
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`
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
Find the angle between the lines whose direction cosines are given by the equations
(i) l + m + n = 0 and l2 + m2 − n2 = 0
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.
Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.
Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.
Write direction cosines of a line parallel to z-axis.
The direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are _______.
Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line `vec("r") = (-2hat"i"+3hat"j") +lambda(2hat"i"-3hat"j"+6hat"k").`Also, find the distance between these two lines.
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
`hat"i" - hat"k"`
If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`, find the magnitude and direction cosines of `3vec"a"- 2vec"b"+ 5vec"c"`
A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.
If the equation of a line is x = ay + b, z = cy + d, then find the direction ratios of the line and a point on the line.
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.
