Advertisements
Advertisements
प्रश्न
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Advertisements
उत्तर
The given direction ratios are a = 3, b = – 1 , c = 3
If a, b, c are the direction ratios of a vector ten the direction cosines of the vector are
l = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
m = `"b"/sqrt("a"^2 + "b"^2 + "c")`
c = `"c"/sqrt("a"^2 + "b"^2 + "c")`
∴ The required direction cosioes of the water are
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`(-1)/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(9 + 1 + 9)`
`(- 1)/sqrt(9 + 1 + 9)`
`3/sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1)/sqrt(9 + 1+ 9))`
`3/sqrt(9 + 1 + 9)`
`1/sqrt(19), (-1)/sqrt(19)`
= `3sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1) /sqrt(19), 3/sqrt(19))`
APPEARS IN
संबंधित प्रश्न
Find the direction cosines of the line
`(x+2)/2=(2y-5)/3; z=-1`
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
Find the acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
What are the direction cosines of X-axis?
What are the direction cosines of Y-axis?
Write the distance of the point (3, −5, 12) from X-axis?
Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
If a unit vector `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with } \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.
A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is
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
If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is
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"`
Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is
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 direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
