Advertisements
Advertisements
Question
Verify whether the following ratios are direction cosines of some vector or not
`4/3, 0, 3/4`
Advertisements
Solution
The given ratios are l = `4/3`, m = 0, n = `3/4`
l2 + m2 + n2 = `(4/3)^2 + 0^2 + (3/4)^2`
= `16/9 + 0 + 9/16`
= `(16 xx 16 + 9 xx 9)/(9 xx 16)`
= `(256 + 81)/144 ≠ 1`
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
∴ The given ratio do not form the direction cosines of a vector.
APPEARS IN
RELATED QUESTIONS
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
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 with direction ratios proportional to 1, −2, 1 and 4, 3, 2.
Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
Write the distance of the point P (x, y, z) from XOY plane.
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.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-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 angle between the two diagonals of a cube is
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"`
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"`
If a line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis is ______.
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 ______.
If a line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.
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 ______.
Any three numbers proportional to the direction cosines of a line are called its:
