Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Answer:
(-8,-2) (-4,6)
Step-by-step explanation:i just got the answer
Answer:
the answers are A, B, C, and F
Step-by-step explanation:
just took the quiz
Answer:
-4 = ?
Step-by-step explanation:
<u>Step 1: Substitute -1 for x</u>
7x^3 + 5x^2 - 2 = ?
7(-1)^3 + 5(-1)^2 - 2 = ?
7(-1) + 5(1) - 2 = ?
-7 + 5 - 2 = ?
-4 = ?
Answer: -4 = ?
