Find an equation of the the line satisfying the given conditions. through (7, 2); perpendicular to 4x + 9y = 46 9x - 4y = 1 • 9x - 4y = 55 4x - y = 55 9x + 4y = 55

  9x - 4y = 55

Step-by-step explanation:

The equation for the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Usually we choose to negate the one that makes the x-coefficient positive. Here, that process gives ...

  9x - 4y = <some constant>

The value of the constant can be found by putting the (x, y) values of the given point into the left-side expression:

  9x - 4y = 9·7 -4·2 = 55

  9x - 47 = 55

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12