133 - FML 3 - 18.1W e.g. 25

Length of a Vector (Vector Norm)

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Given the vector v⃗=<v1,v2,v3>\bcb{\vec{v} = \left<v_1, v_2, v_3 \right>}v=⟨v1​,v2​,v3​⟩, find an expression for its length in terms of its components v1, v2,\bcb{v_1,\, v_2,}v1​,v2​, and v3\bcb{v_3}v3​.

	

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More Length of a Vector (Vector Norm) Questions:

Write the vectors𝑢⃗=(1,2,3)𝑢⃗=(1,2,3)u⃗=(1,2,3), 𝑣⃗=(5,−2,2)𝑣⃗=(\sqrt{5},−2,2)v⃗=(5​,−2,2), and  𝑤⃗=(3,3,3)\ 𝑤⃗=(\sqrt{3},\sqrt{3},3) w⃗=(3​,3​,3) in increasing order of length.
(i.e. shortest vector first)

Vectors and coordinates (Components of a vector)

In diagram below two vectors A⃗\vec{A}Aand B⃗\vec{B}B have shown. VectorsC⃗\vec{C}Cand D⃗\vec{D}Dare the sum (A⃗+B⃗)\left(\vec{A}+\vec{B}\right)(A+B) and difference (A⃗−B⃗)\left(\vec{A}-\vec{B}\right)(A−B)vectors, respectively. 
Which statement is correct about the magnitude of four vectors?

Practice Question: Properties of Vector Operations

Practice Question: Properties of Vector Operations
If u⃗, v⃗, w⃗ ∈R3\vec{u},\ \vec{v},\ \vec{w}\ \in R^3u, v, w ∈R3, which of the following statements is/are always true?
i.) ∣∣v⃗−u⃗∣∣=−∣∣u⃗−v⃗∣∣\left|\left|\vec{v}-\vec{u}\right|\right|=-\left|\left|\vec{u}-\vec{v}\right|\right|∣∣v−u∣∣=−∣∣u−v∣∣

Practice: Magnitude of a 3D Vector

Practice: Magnitude of a 3D Vector
An aircraft's location is 200 miles S30oW from base, and it's altitude is 35,000 ft. Find the distance between the aircraft and the base.

$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | $\tkco{duplicate to mock ✓}$ 133 - FML 3 - 18.1W e.g. 46_$\tkcth{Mock F}\tkct{?}$_$\tkct{vid soln only}$

If ∣u⃗∣=2\bcb{|{\vec{u}|} = 2}∣u∣=2 and ∣v⃗∣=3\bcb{|{ \vec{v} |} = 3}∣v∣=3, where u⃗⋅v⃗=2\bcb{\vec{u} \cdot \vec{v} = 2}u⋅v=2, find ∣u⃗−v⃗∣\bcb{|{\vec{u} - \vec{v} }|}∣u−v∣.

133 - FML 3 - 18.1W e.g. 25

Given the vector v⃗=<v1,v2,v3>\bcb{\vec{v} = \left<v_1, v_2, v_3 \right>}v=⟨v1​,v2​,v3​⟩, find an expression for its length in terms of its components v1, v2,\bcb{v_1,\, v_2,}v1​,v2​, and v3\bcb{v_3}v3​.

Length / magnitude / norm. 19.1W

1. Find the vector d⃗\vdd connecting the points P1(−2,−1)P_1(-2,-1)P1​(−2,−1) and P2(3,11)P_2(3,11)P2​(3,11).
2. Find the length of the vector d⃗\vdd found, above. What does this length represent? 

Given that the length of 𝑣⃗=(−3,𝑘)\vec{𝑣}=(−3,𝑘)v=(−3,k) is 5, find all possible values of 𝑘.

Practice Question: Properties of Vector Operations

Practice Question: Properties of Vector Operations
If u⃗, v⃗, w⃗ ∈R3\vec{u},\ \vec{v},\ \vec{w}\ \in R^3u, v, w ∈R3, which of the following statements is/are always true?
i.) ∣∣v⃗−u⃗∣∣=−∣∣u⃗−v⃗∣∣\left|\left|\vec{v}-\vec{u}\right|\right|=-\left|\left|\vec{u}-\vec{v}\right|\right|∣∣v−u∣∣=−∣∣u−v∣∣

Practice Question: Vector Operations and Length

Practice Question: Properties of Vector Operations
If u⃗, v⃗, w⃗ ∈R3\vec{u},\ \vec{v},\ \vec{w}\ \in R^3u, v, w ∈R3, which of the following statements is/are always true?
i.) ∣∣v⃗−u⃗∣∣=−∣∣u⃗−v⃗∣∣\left|\left|\vec{v}-\vec{u}\right|\right|=-\left|\left|\vec{u}-\vec{v}\right|\right|∣∣v−u∣∣=−∣∣u−v∣∣

Practice: Norm of a Vector

Which of the following statements are true:
There exist vectors such that ∥u⃗+v⃗∥=∥u⃗∥+∥v⃗∥\|\vec{u}+\vec{v}\|=\|\vec{u}\|+\|\vec{v}\|∥u+v∥=∥u∥+∥v∥
If ∥u⃗∥=∥v⃗∥\|\vec{u}\|=\|\vec{v}\|∥u∥=∥v∥ then u⃗=v⃗\vec{u}=\vec{v}u=v

Vector Norm

Practice: Properties of the Norm
Consider u⃗, v⃗, w⃗ ∈Rn\vec{u},\ \vec{v},\ \vec{w}\ \in \reals^nu, v, w ∈Rn. Select all of the statements that are always true.

Vector Norm

Practice: Distance Between Two Points/Vectors

Vector Norm

Practice: Vector Length
Given  v⃗=[−3k]\vec{v}=
\begin{bmatrix}
  -3\\ k\\
\end{bmatrix}v=[−3k​] and  ∥v⃗∥=5\lVert \vec v \rVert = 5∥v∥=5 , find all possible values of kkk.

Practice Question: Vector Length

Practice Question: Vector Length
Given that the length of 𝑣⃗=(−3,𝑘)\vec{𝑣}=(−3,𝑘)v=(−3,k) is 5, find all possible values of 𝑘.

Length of a Vector

Practice: Vector Length

Practice: Vector Length
Given that the length of 𝑣⃗=(−3,𝑘)\vec{𝑣}=(−3,𝑘)v=(−3,k) is 5, find all possible values of 𝑘.

$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ |

The distance between the points P1(2,−3,7)P_1(2,-3,7)P1​(2,−3,7) and P2(4,3,16)P_2(4,3,16)P2​(4,3,16) is: 

Dot and Cross Products: Vector Norm

If u⃗, v⃗, w⃗  ∈ R3\vec{u},\ \vec{v},\ \vec{w}\ \ \in\ R^3u, v, w  ∈ R3, which of the following operations is/are defined?
(i.e. which of the following can be calculated?)
Select all that are correct.

Vector Norm: Length of a Vector

Find ∥v∥\lVert \bm{v} \rVert∥v∥ where v=(2,3,−3,−4,0)\bm{v}=(\sqrt 2,3,-3,-4,0)v=(2​,3,−3,−4,0)

133 - FML 3 - 18.1W e.g. 25

Related Topics

Length of a Vector (Vector Norm)

Given the vector $\bcb{\vec{v} = \left<v_1, v_2, v_3 \right>}$ , find an expression for its length in terms of its components $\bcb{v_1,\, v_2,}$ and $\bcb{v_3}$ .

More Length of a Vector (Vector Norm) Questions:

Vectors and coordinates (Components of a vector)

Practice Question: Properties of Vector Operations

Practice: Magnitude of a 3D Vector

$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | $\tkco{duplicate to mock ✓}$ 133 - FML 3 - 18.1W e.g. 46_$\tkcth{Mock F}\tkct{?}$_$\tkct{vid soln only}$

133 - FML 3 - 18.1W e.g. 25

Length / magnitude / norm. 19.1W

Practice Question: Properties of Vector Operations

Practice Question: Vector Operations and Length

Practice: Norm of a Vector

Vector Norm

Vector Norm

Vector Norm

Practice Question: Vector Length

Length of a Vector

Practice: Vector Length

$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ |

Dot and Cross Products: Vector Norm

Vector Norm: Length of a Vector

133 - FML 3 - 18.1W e.g. 25

Related Topics

Length of a Vector (Vector Norm)

Given the vector v⃗=<v1,v2,v3>\bcb{\vec{v} = \left<v_1, v_2, v_3 \right>}v=⟨v1​,v2​,v3​⟩, find an expression for its length in terms of its components v1, v2,\bcb{v_1,\, v_2,}v1​,v2​, and v3\bcb{v_3}v3​.

More Length of a Vector (Vector Norm) Questions:

Vectors and coordinates (Components of a vector)

Practice Question: Properties of Vector Operations

Practice: Magnitude of a 3D Vector

$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | $\tkco{duplicate to mock ✓}$ 133 - FML 3 - 18.1W e.g. 46_$\tkcth{Mock F}\tkct{?}$_$\tkct{vid soln only}$

133 - FML 3 - 18.1W e.g. 25

Length / magnitude / norm. 19.1W

Practice Question: Properties of Vector Operations

Practice Question: Vector Operations and Length

Practice: Norm of a Vector

Vector Norm

Vector Norm

Vector Norm

Practice Question: Vector Length

Length of a Vector

Practice: Vector Length

$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ |

Dot and Cross Products: Vector Norm

Vector Norm: Length of a Vector

Given the vector $\bcb{\vec{v} = \left<v_1, v_2, v_3 \right>}$ , find an expression for its length in terms of its components $\bcb{v_1,\, v_2,}$ and $\bcb{v_3}$ .