Question

decompose the vector b=6i-3j-6k into two vectors c and d one of which is parallel and the other perpendicular to the vector b=i+j+k

Answer 1

Answer:

c = -i - j - k

d = 7i -2j -5k

Step-by-step explanation:

Given b = 6i - 3j - 6k  and  a = i + j + k.

We want to write

    b = c + d

where c is parallel to a and d is perpendicular to a.

For this, we need c to be the projection of b onto a.

So        c = [ ( b · a ) / ( a · a ) ] a.

Now  b · a = 6 - 3 - 6 = -3  and  a · a = 1 + 1 + 1 = 3.

So ( b · a ) / ( a · a ) = -3/3 = -1.

Therefore c = -a = -i - j - k

and d = b - c = ( 6i - 3j - 6k ) - ( -i - j - k ) = 7i -2j -5k.

Check that these are perpendicular:

c · d = -7 + 2 + 5 = 0.  Yes!!

Answer 2

Answer:

wrong processnbro

Step-by-step explanation:

1. i am thinking