3. Vectors

Given two vectors $j-k$ and $k-i$, what is their cross product $\times$ using the properties of cross products (not determinants)?

Using the properties of cross products, what is the result of $i\times j$×$k$?

Given two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle $\theta$ between them, what is the magnitude of their vector product $|\overrightarrow{a}\times \overrightarrow{b}|$?

Given the vectors $a=t𝑖+\cos \left(t\right)𝑗+\sin \left(t\right)𝑘$ and $b=𝑖-\sin \left(t\right)𝑗+\cos \left(t\right)𝑘$, what is the cross product $a\times b$?

Find the magnitude and direction of the vector C =2B × A.

(I) If vector A→ points along the negative x axis and vector B→ along the positive z axis, what is the direction of (a) A→ x B→ and (b) B→ x A→? (c) What is the magnitude of A→ x B→ and B→ x A→?

For two non-parallel vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, the cross product $\overrightarrow{a}\times \overrightarrow{b}$ points in which direction?

Given two vectors $a$ and $b$ in three-dimensional space, which of the following statements correctly describes the cross product $a\times b$ using its properties (without using determinants)?

(I) The directions of vectors $\vec{A}$ and $\vec{B}$ are given below for several cases. For each case, state the direction of $\vec{A}\times \vec{B}$. $\vec{A}$ points straight up, $\vec{B}$ points straight down.

What is the magnitude of the cross product of two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$?

Let $u=\left(3,0,0\right)$ and $v=\left(0,4,0\right)$. What is $|u\times v|$ and is $u\times v$ directed into the screen or out of the screen?

Given the vectors $i+j$ and $i-j$, what is the result of their cross product $\times$ using the properties of cross products (not determinants)?

(I) The directions of vectors A → and B→ are given below for several cases. For each case, state the direction of A→ x B→ . (d) A→ points straight up, B→ points straight down.

For the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ in the figure$1.39$, find the magnitude and direction of the vector product $\overrightarrow{A}\times \overrightarrow{B}$.

(II) Determine (a) the vector product A→ x B→ and (b) the angle between A→ and B→ if A→ = 7.4î - 3.5ĵ and B→ = -8.5î + 4.6ĵ + 2.0k̂ . [Hint: To resolve an ambiguity, the dot product may prove useful.]