Cross Product Properties

5 Activities

Practice: Cross Product Properties
Let u⃗, v⃗, w⃗∈R3\vec u ,\ \vec{v} ,\  \vec w \in \reals^3u, v, w∈R3 be vectors.
Let c, d∈Rc,\ d \in \realsc, d∈R be scalars.

Select all of the following that produce a vector.

A) (𝑤⃗×𝑐𝑢⃗)+𝑑𝑣⃗(\vec𝑤× 𝑐𝑢⃗ ) + 𝑑\vec𝑣(w×cu⃗)+dv

B) (w⃗×cu⃗)⋅dv⃗\left(\vec{w}\times c\vec{u}\right)\cdot d\vec{v}(w×cu)⋅dv

C) (cu⃗⋅v⃗)(w⃗×dv⃗)(c\vec{u}\cdot \vec{v})(\vec{w}\times d\vec{v})(cu⋅v)(w×dv)

D) cu⃗⋅d(v⃗×w⃗)c\vec{u} \cdot d(\vec{v} \times\vec{w})cu⋅d(v×w)

I don't know

Practice Question: Dot and Cross Product Properties

Practice Question: Dot and Cross Product Properties
Given that u⃗=(1,−2,0,1)\vec{u}=\left(1,-2,0,1\right)u=(1,−2,0,1) and 𝑣⃗\vec𝑣 v =(0,1,2,1),=(0,1,2,1),=(0,1,2,1), which of the following is true?

𝑢⃗,𝑣⃗,𝑤⃗𝑢⃗ ,\vec{𝑣} , \vec𝑤u⃗,v,w are vectors in R3ℝ^3R3 and 𝑐, 𝑑 are scalars. Which of the following produce(s) a vector?
i) (𝑤⃗×𝑐𝑢⃗)+𝑑𝑣⃗(\vec𝑤× 𝑐𝑢⃗ ) + 𝑑\vec𝑣(w×cu⃗)+dv
ii) (w⃗×𝑐𝑢⃗)⋅𝑑𝑣(\vec{w}×𝑐𝑢⃗   ) \cdot 𝑑𝑣(w×cu⃗)⋅dv

Practice Question: Properties of Dot and Cross Products

Practice Question: Properties of Dot and Cross Products
𝑢⃗,𝑣⃗,𝑤⃗𝑢⃗ ,\vec{𝑣} , \vec𝑤u⃗,v,w are vectors in R3ℝ^3R3 and 𝑐, 𝑑 are scalars. Which of the following produce(s) a vector?
i) (𝑤⃗×𝑐𝑢⃗)+𝑑𝑣⃗(\vec𝑤× 𝑐𝑢⃗ ) + 𝑑\vec𝑣(w×cu⃗)+dv

Practice Question: Vector Properties

Practice Question: Vector Properties
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?)

Practice: Dot and Cross Product Properties

Practice: Dot and Cross Product Properties
𝑢⃗,𝑣⃗,𝑤⃗𝑢⃗ , \vec𝑣 , 𝑤⃗u⃗,v,w⃗ are vectors in R3ℝ^3R3 and 𝑐, 𝑑 are scalars. Which of the following is/are true?

Practice: Cross Product (1)

Do the vectors u⃗= <3, −1, 4>, v⃗= <6, 0, 1>, and w⃗= <−1, 2, 5> \vec{u}=~<3,~-1,~4>,~\vec{v}=~<6,~0,~1>,~\text{and}~\vec{w}=~<-1,~2,~5>~u= <3, −1, 4>, v= <6, 0, 1>, and w= <−1, 2, 5> lie in the same plane?

$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 51_$\tkcth{Mock F}\tkct{?}$_$\tkct{no soln / vid}$

 If u⃗=<1,−2,3>\bcb{\vec{u} = \left< 1, -2, 3 \right>}u=⟨1,−2,3⟩ and v⃗=<2,−1,3>\bcb{\vec{v} = \left< 2, -1, 3 \right>}v=⟨2,−1,3⟩ then u⃗×v⃗\bcb{\vec{u} \times \vec{v}}u×v is parallel to:

Additional practice problems--vector products

Additional Practice Problems--Vector Products
1. If u⃗=(−2,3,−1),  v⃗=(−1,−2,3)\vec{u}=\left(-2,3,-1\right),\ \ \vec{v}=\left(-1,-2,3\right)u=(−2,3,−1),  v=(−1,−2,3), find
a) u⃗ ∙ v⃗\vec{u}\ \bullet\ \vec{v}u ∙ v

Given that u→\overrightarrow{u}u, v→\overrightarrow{v}vand w→\overrightarrow{w}ware vectors in R3\mathbb{R}^3R3and kkkis a scalar (constant). Which of the following operations are defined (possible)?
u→⋅(v→×w→)\overrightarrow{u}\cdot(\overrightarrow{v}\times\overrightarrow{w})u⋅(v×w)
u→+(v→⋅w→)\overrightarrow{u}+(\overrightarrow{v}\cdot\overrightarrow{w})u+(v⋅w)

Cross Product Properties

Related Topics

Cross Product Properties

Practice: Cross Product Properties

More Cross Product Properties Questions:

Practice Question: Dot and Cross Product Properties

Practice Question: Properties of Dot and Cross Products

Practice Question: Vector Properties

Practice: Dot and Cross Product Properties

Practice: Cross Product (1)

$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 51_$\tkcth{Mock F}\tkct{?}$_$\tkct{no soln / vid}$

Additional practice problems--vector products