Find a vector equation for the line passing through the point (5,-1) and perpendicular to the vector i+j?

Answer 1

If two vectors are perpendicular their dot product is zero. Let the vector of the perpendicular line be given by

v = ai + bj =

• <1, 1> = a + b = 0
a = -b

Reduced to lowest terms, = <1, -1>.

The vector equation of the line then is:

L = <5, -1> + t<1, -1>
where t is a scalar ranging over the real numbers.

Answer 2

the vector i+j is y=x,
so the equation of your line must be
y=-x+a
then, it pass through (5; -1)
so -1=-5+a
a=-1+5
a=4
the vector equation is y= -x + 4