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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
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.
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