Express the following vector in the form v vi+V2j+ v3k 3u -v if u (3,5,-8) and v (2,-5,7)

Step-by-step explanation:

Given the vectors u (3,5,-8) and v (2,-5,7), they can also be written as;

u = 3i+5j-8k

v = 2i-5j+7k

To express the vector 3u - v in vector form, first let us find the vector 3u;

3u = 3(3i+5j-8k)

3u = 3(3i)+3(5j)-3(8k)

3u = 9i+15j-24k

Subtract v from the resulting vector.

Since v =  2i-5j+7k

3u - v = 9i+15j-24k - (2i-5j+7k)

3u-v = 9i+15j-24k -2i+5j-7k

collect the like terms

3u-v = 9i-2i+15j+5j-24k-7k

3u-v = 7i+20j-31k

Hence the vector 3u-v in the form v =  vi+V2j+ v3k is 7i+20j-31k

the answer is 62.8 cubic units