Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
उत्तर
The direction ratio of the vector `3hat"i" - 3hat"k" + 4hat"j"` are (3, 4, – 3)
The direction cosines of the vector `3hat"i" - 3hat"k" + 4hat"j"` are
`3/sqrt(3^2 + 4^2 + (-3)^2), 4/sqrt(3^2 + 4^2 + (-3)^2), (-3)/sqrt(3^2 +4^2 + (-3)^2)`
`3/sqrt(9 + 16 + 9), 4/sqrt(9 + 16 + 9), (-3)/sqrt(9 + 16 + 9)`
`(3/sqrt(34), 4/sqrt(34), (-3)/sqrt(34))`
Direction ratios = (3, 4, – 3)
Directio cosines = `(3/sqrt(34), 4/sqrt(34), (-3)/sqrt(34))`
APPEARS IN
संबंधित प्रश्न
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).
Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.
Write the distance of the point (3, −5, 12) from X-axis?
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
Write direction cosines of a line parallel to z-axis.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c
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 ______.
The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are ______.
A line in the 3-dimensional space makes an angle θ `(0 < θ ≤ π/2)` with both the x and y axes. Then the set of all values of θ is the interval ______.
The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
