Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Let A be the point (1, 0, 0) and B be the point (0, 1, 0)
(i.e.,) `vec"OA" = hat"i"` and `vec"OB" = hat"j"`
Then `vec"AB" = vec"OB" - vec"OA"`
= `hat"j" - hat"i"`
= `-hat"i" + hat"j"`
= (– 1, 1, 0)
= (a, a + b, a + b + c)
⇒ a = – 1, a + b = 1 and a + b + c = 0
Now a = – 1
⇒ – 1 + b = 1
a + b + c = 0
⇒ b = 2
– 1 + 2 + c = 0
⇒ c + 1 = 0
⇒ c = – 1
∴ a = – 1, b = 2, c = – 1.
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 Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).
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 cosines are given by the equations
l + 2m + 3n = 0 and 3lm − 4ln + mn = 0
Write the distance of the point (3, −5, 12) from X-axis?
Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"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 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.
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 ______.
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 ______.
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
The d.c's of a line whose direction ratios are 2, 3, –6, are ______.
The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be ______.
