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.
The Cartesian equation of the line is '
`(x-5)/3 = (y+4)/7 = ("z"-6)/2` ...(1)