p = 2i + 3j + 4k
q = i + 3j + 2k
r = 2i + j + ak
If p.(q+r) is 6 greater than q.(p+r) find the value of a.
This is what I've done so far.
p.(q+r) = 4a + 26
q.(p+r) = 2a + 24
Can you tell me the next step of this? Thanks
Answer: 2
i don't really like to work in the i-j-k notation, so let's write
p = <2,3,4>
q = <1,3,2>
r = <2,1,a>
i suppose your dot means the dot product
Now, p.(q + r) = <2,3,4>.(<1,3,2> + <2,1,a>)
....................= <2,3,4>.<3,4,2+a>
....................= 6 + 12 + 8 + 4a
....................= 26 + 4a
Now, q.(p + r) = <1,3,2>.(<2,3,4> + <2,1,a>)
....................= <1,3,2>.<4,4,4+a>
....................= 4 + 12 + 8 + 2a
....................= 24 + 2a
Now we are told that p.(q+r) is 6 greater than q.(p+r), that is,
q.(p + r) + 6 = p.(q + r)
=> 24 + 2a + 6 = 26 + 4a
=> 2a = 4
=> a = 2