T1W10L1: geometrical proof using vectors

god. this is awful. proofs, AND vectors? two of the worst portions of maths in existence. I am going to get a 20% in this test. ABSOLUTELY awful. geometrical proofs at that.

i love proofs. i love vectors. i love geometrical proofs. i love asa ass sas sss !!!!

facts of vector algebra you can use: §

• $a=b$ if and only if $a$ and $b$ have the same magnitude and direction
• $-a$ has the same magnitude as $a$ but the opposite direction6
• for a scalar $\lambda >0$, $\lambda a$ has magnitude $\lambda |a|$ and the same direction as $a$
• if $a=\lambda b$ then if $\lambda >0$, $a$ and $b$ are like parallel vectors; otherwise if $\lambda <0$, $a$ and $b$ are unlike parallel vectors.
• vectors can be added using a triangle of vectors
• $a-b=a+(-b)$
• if $\lambda$ is a scalar, then $\lambda (a+b)=\lambda a+\lambda b$
• $a\perp b$ if and only if $a\cdot b=0$