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प्रश्न
f the straight line joining the points (2, 1, 4) and (a – 1, 4, – 1) is parallel to the line joining the points (0, 2, b – 1) and (5, 3, – 2) find the values of a and b
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उत्तर
(i) Points are (2, 1, 4)(a – 1, 4, – 1)
Cartesian equation
`(x - x_1)/(x_2 - x_1) = (y - y_1)/(y_2 - y_1) = (z - z_1)/(z_2 - z_1)`
⇒ `(x - 2)/("a" - 1 - 2) = (y - 1)/(4 - 1) = (z - 4)/(-1 - 4)`
⇒ `(x - 2)/("a" - 3) = (y - 1)/3 = (z - 4)/(-5)`
(ii) Points are (0, 2, b – 1)(5, 3, – 2)
Cartesian equation
⇒ `(x - 5)/5 = (y - 2)/(3 - 2) = (z - "b" + 1)/(-2 - "b" + 1)`
⇒ `x/5 = (y - 2)/1 = (z - "b" + 1)/(- "b" - 1)`
If they ae parallel
`"b"_1/"d"_1 = "b"_2/"d"_2 = "b"_3/"d"_3`
`("a" - 3)/5 = 3/1 = (-5)/(- "b" - 1)`
`("a" - 3)/5` = 3, `(-5)/(- "b" - 1)` = 3
a = 15 + 3, `5/("b" + 1)` = 3
a = 18, b + 1 = `5/3`
⇒ b = `5/3 - 1 = 2/3`
b = `2/3`
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