Question

Compute the following cross products. Then make a sketch showing the two vectors and their cross product. $- \mathbf { j } \times \mathbf { k }$

Solution

Verified
Step 1
1 of 4

The magnitude of a cross product of vectors $\mathbf u$ and $\mathbf v$ is defined as

$|\mathbf u \times \mathbf v|=|\mathbf u| |\mathbf v| \sin \angle (\mathbf u, \mathbf v)$

The vector $\mathbf u \times \mathbf v$ is orthogonal to both vectors $\mathbf u$ and $\mathbf v$. Its direction is determined by the right-hand rule, which means, when putting $\mathbf u$ and $\mathbf v$ to start at the same point and let the fingers of a right hand to curl from $\mathbf u$ to $\mathbf v$, the thumb points to the direction of a cross product $\mathbf u \times \mathbf v$.

Recommended textbook solutions

Biology

1st EditionISBN: 9780132013499Kenneth R. Miller, Levine
2,470 solutions

Calculus: Early Transcendentals

3rd EditionISBN: 9780134763644 (4 more)Bernard Gillett, Eric Schulz, Lyle Cochran, William L. Briggs
13,402 solutions

Nelson Science Perspectives 10

1st EditionISBN: 9780176355289Christy C. Hayhoe, Doug Hayhoe, Jeff Major, Maurice DiGiuseppe
1,359 solutions

Miller and Levine Biology

1st EditionISBN: 9780328925124 (2 more)Joseph S. Levine, Kenneth R. Miller
1,773 solutions