Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर १
The direction ratios of the given lines are – 3, 2k, 2 and 3k, 1, −5.
∵ If the lines are perpendicular then a1a2 + b1b2 + c1c2 = 0
∴ – 3.3k + 2k.1 + 2.( –5) = 0
⇒ 9k + 2k – 10 = 0
⇒ −7k = 10
k = `(-10)/7`
उत्तर २
The given lines are,
`(x - 1)/-3 = (y - 2)/(2k) = (z - 3)/2` ....(i)
and `(x - 1)/(3k) = (y - 1)/1 = (z - 6)/-5` ....(ii)
The direction ratio of the line (i) are < - 3, 2k, 2 >
The direction ratio of the line (ii) are < 3k, 1, -5 >
if -9k + 2k - 10 = 0 if 7k = -10 if `k = -10/7`
APPEARS IN
संबंधित प्रश्न
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
Find the direction cosines of a line which makes equal angles with the coordinate axes.
Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1.
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
If a line makes angles of 90°, 60° and 30° with the positive direction of x, y, and z-axis respectively, find its direction cosines
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
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.
What are the direction cosines of X-axis?
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
Write direction cosines of a line parallel to z-axis.
For every point P (x, y, z) on the x-axis (except the origin),
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 α, β, γ, δ with four diagonals of a cube, then cos2 α + cos2 β + cos2γ + cos2 δ is equal to
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Verify whether the following ratios are direction cosines of some vector or not
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
Find the direction cosines and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
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"`
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
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.
If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.
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 ______.
The d.c's of a line whose direction ratios are 2, 3, –6, are ______.
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
