Advertisements
Advertisements
प्रश्न
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
Advertisements
उत्तर
The given ratios are l = `1/5`, m = `3/5`, n = `4/5`
l2 + m2 + n2 = `(1/5)^2 +(3/5)^2 + (4/5)^2`
= `1/25 + 9/25 + 16/25`
= `(1 + 9 + 16)/25`
= `26/25 ≠ 1`
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
∴ The given ratio `1/5, 3/5, 4/5` do not form the direction cosines of a vector.
APPEARS IN
संबंधित प्रश्न
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
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 − m + 2n = 0 and mn + nl + lm = 0
Define direction cosines of a directed line.
What are the direction cosines of Z-axis?
A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.
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.
Find the distance of the point (2, 3, 4) from the x-axis.
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
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
The distance of the point P (a, b, c) from the x-axis is
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
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.
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`
The area of the quadrilateral ABCD, where A(0,4,1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.
Which identity must be satisfied by the direction cosines \[(l,m,n)\] of a line?
For the line directed from \[P(x_1,y_1,z_1)\] to \[Q(x_2,y_2,z_2)\], which expression is the direction cosine \[m\]?
