-20 - 90v
10(-2-9v) multiply each term in parentheses by 10
-10 × 2 - 10 × 9v multiply the numbers
-20 - 10 × 9v calculate the product
-20 - 90v is the answer
we find our area to find area we multiply thoses numbers to get our answer so our area is 192
the value of v.w= -12.
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:
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
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)
hence, v.w= -12