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
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
For every point P (x, y, z) on the xy-plane,
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
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
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 `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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 `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 `vec"a", vec"b", vec"c"`
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
The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
If the directions cosines of a line are k,k,k, then ______.
A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
