💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Show that $ 0 \times a = 0 = a \times 0 $ for any vector $ a $ in $ V_3 $.

See explanation.

01:29

Wen Z.

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 4

The Cross Product

Vectors

Johns Hopkins University

Campbell University

Baylor University

University of Nottingham

Lectures

02:56

In mathematics, a vector (…

06:36

02:00

Show that $ (a \times b) \…

01:51

Show that $(\mathbf{a} \ti…

02:58

Show that $\vec{A} \cdot(\…

00:33

Prove the following for an…

02:50

Determine whether the foll…

01:31

Suppose that you are given…

02:37

Show that the given vector…

01:21

For any vector $\mathbf{v}…

03:21

Suppose $\mathbf{u}$ and $…

02:19

Given the three nonzero ve…

Mhm. Let's do another cross product problem where we're trying to show that a cross zero equals zero, no matter what factor is. This is one of the properties of cross products. But we can verify this by taking an arbitrary vector A defined to be a one A two, A three. There's going to be any numbers. And looking at what happens when we take the cross product with the zero vector 000 Using the technique from our textbook, we can ignore the first column and look at A two time 0 minus a three time zero. Hi minus next. We'll ignore our second column and look at a one time zero -3 times zero. And turn off and lastly sorry, that LBJ. And then lastly, we'll ignore our third column. Look at a one time 0 minus a two time zero, which gives us the vector zero, I plus zero J plus zero K. Which we can just call the big old zero vector. Similarly, if we want to look at what happens when we look at zero cross A. Again, we're expecting this to be zero because that's one of the properties of cross products. Let's do the same thing A one A two, A three. And if we do our math again, ignore the first column zero times a three minus zero times a two, second column, zero times a 3 0 times a one zero. And lastly zero times A to write a zero times a one just like before we get zero in every term, no matter what the values of a one, A two And a three r. Because a cross zero is equal to zero. Cross a Is equal to the zero vector. Thanks for watching.

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Show that $ (a \times b) \cdot b = 0 $ for all vectors $ a $ and $ b $ in $ …

Show that $(\mathbf{a} \times \mathbf{b}) \cdot \mathbf{b}=0$ for all vector…

Show that $\vec{A} \cdot(\vec{A} \times \vec{B})=0$ for any vectors $\vec{A}…

Prove the following for any vector $\mathbf{u :} \quad 0 \cdot \mathbf{u}=0$…

Determine whether the following statements are true using a proof or counter…

Suppose that you are given a vector $\mathbf{u} .$ For what vectors $\mathbf…

Show that the given vector functions are linearly dependent on $(-\infty, \i…

For any vector $\mathbf{v}$ in $\mathbb{R}^{3},$ explain why $\mathbf{v} \ti…

Suppose $\mathbf{u}$ and $\mathbf{v}$ are nonzero vectors in $\mathbb{R}^{3}…

Given the three nonzero vectors $\mathbf{A}, \mathbf{B},$ and $\mathbf{C},$ …