Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Show that the line through points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (−1, −2, 1) and (1, 2, 5).
Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
For every point P (x, y, z) on the x-axis (except the origin),
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 `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 the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
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 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 ______.
O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.
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 ______.
A directed line makes angles \[\alpha\], \[\beta\], and \[\gamma\] with the positive x-, y-, and z-axes respectively. What are these angles called?
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
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 \[m\]?
