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प्रश्न
Find the parametric form of vector equation and Cartesian equations of the straight line passing through the point (– 2, 3, 4) and parallel to the straight line `(x - 1)/(-4) = (y + 3)/5 = (8 - z)/6`
उत्तर
`vec"a" = -2hat"i" + 3hat"j" + 4hat"k" (x_1 y_1, z_1)` = (– 2, 3, 4)
`vec"b" = - 4hat"i" + 5hat"j" + 6hat"k" (l, "m", "n")` = (– 4, 5, 6)
Vector equation
`vec"r" = vec"a" + "t"vec"b"`, t ∈ R
`vec"r" = (-2hat"i" + 3hat"j" + 4hat"k") + "t"(-4hat"i" + 5hat"j" - 6hat"k")`, t ∈ R
Cartessain equation
`(x - x_1)/1 = (y - y_1)/"m" = (z - z_1)/"n"`
`(x + 2)/(-4) = (y - 3)/5 = (z - 4)/(- 6)`
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