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The Cartesian Equation of a Line is `(X-5)/3 = (Y+4)/7 = ("Z"-6)/2` Write Its Vector Form. - Mathematics

The Cartesian equation of a line is `(x-5)/3 = (y+4)/7 = ("z"-6)/2` Write its vector form.

The given line passes through the point (5, −4, 6). The position vector of this point is `veca = 5hati - 4hatj + 6hatk`

Also, the direction ratios of the given line are 3, 7, and 2.

This means that the line is in the direction of vector, `vecb =3hati +7hatj + 2hatk`

It is known that the line through position vector `veca` and in the direction of the vector `vecb`is given by the equation, `vecr = veca+lambdavecb, lambda in R`

This is the required equation of the given line in vector form.

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Solution

The Cartesian equation of the line is '

`(x-5)/3 = (y+4)/7 = ("z"-6)/2`   ...(1)

 

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APPEARS IN

NCERT Class 12 Maths
Chapter 11 Three Dimensional Geometry
Q 7 | Page 477
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