Answer: The required value of the given expression is -204.
Step-by-step explanation: We are given the following two vectors :
[tex]u=-8i+3j,\\\\v=6i-j.[/tex]
We are to find the value of the following :
[tex](u+v)^2-(u-v)^2.[/tex]
We will be using the following identities :
[tex]i.j=j.i=0,\\\\i^2=j^2=1.[/tex]
Therefore, the value of the given expression can be evaluated as follows :
[tex](u+v)^2-(u-v)^2\\\\=(u^2+2uv+v^2)-(u^2-2uv+v^2)\\\\=4uv\\\\=4(-8i+3j)(6i-j)\\\\=4(-48i^2+8ij+18ji-3j^2)\\\\=4(-48\times1-3\times1)\\\\=4(-48-3)\\\\=-204.[/tex]
Thus, the required value of the given expression is -204.
