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
If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
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
2l + 2m − n = 0, mn + ln + lm = 0
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians
If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
Find the direction cosine of a line which makes equal angle with coordinate axes.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.
The d.c's of a line whose direction ratios are 2, 3, –6, are ______.
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.
For direction ratios \[(a,b,c)\], which set can represent the corresponding direction cosines when the direction of the line is chosen?
In the relation between direction ratios and direction cosines, what does the sign \[\pm\] in \[l=\pm\frac{a}{\sqrt{a^2+b^2+c^2}}\] depend on?
