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A line passes through the point with ...

A line passes through the point with position vector `2 hat i-3 hat j+4 hat k` and is in the direction of `3 hat i+4 hat j-5 hat kdot` Find the equations of the line in vector and Cartesian forms.

Text Solution

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Since the line passes through `2hati-3hatj+4hatk` and has direction of `3hati+4hatj-5hatk`, its vector equation is
`" "vecr=hata+lamdahatbrArrvecr=2hati-3hatj+4hatk+lamda(3hati+4hatj-5hatk)`, where `lamda` is a parameter.`" "`(i)
Cartesian equivalent of (i) is `(x-2)/(3)=(y+3)/(4)=(z-4)/(-5)`
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