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Find the vector equation of the line which is parallel to the vector `3hati-2hatj+6hatk` and which passes through the point `(1,-2,3)`. |
Answer» Let `veca=3hati-2hatj+6hatk` and `vecb=hati-2hatj+3hatk` so, vector equation of the line, which is parallel to the vector `veca=3hati-2hatj+6hatk` and passes through the vector `vecb=hati-2hatj+3hatk` is `vecr=vecb+lamdaveca` `:. vecr=(hati-2hatj+3hatk)+lamda(3hati-2hatj+6hatk)` `implies (xhati+yhatj+zhatk)-(hati-2hatj+3hatk)=lamda(3hati-2hatj+6hatk)` `implies (x-1)hati+(y+2)hatj+(z-3)hatk=lamda(3hati-2hatj+6hatk)` |
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