I was just messing around on this calculator when I pressed shift and found that the pound sign had a button on the calculator. Since then, I have been wondering about what it does. Could someone please answer this?

helperid1839321
Apr 6, 2017

#1**0 **

Compute the following cross product:

(1, 2, 3)x(4, 5, 6), where # = x

Construct a matrix where the first row contains unit vectors i^^, j^^, and k^^; and the second and third rows are made of vectors (1, 2, 3) and (4, 5, 6):

(i^^ | j^^ | k^^

1 | 2 | 3

4 | 5 | 6)

Take the determinant of this matrix:

left bracketing bar i^^ | j^^ | k^^

1 | 2 | 3

4 | 5 | 6 right bracketing bar

Expand with respect to row 1:

left bracketing bar i^^ | j^^ | k^^

1 | 2 | 3

4 | 5 | 6 right bracketing bar

The determinant of the matrix (i^^ | j^^ | k^^

1 | 2 | 3

4 | 5 | 6) is given by i^^ left bracketing bar 2 | 3

5 | 6 right bracketing bar + (-j^^) left bracketing bar 1 | 3

4 | 6 right bracketing bar + k^^ left bracketing bar 1 | 2

4 | 5 right bracketing bar :

i^^ left bracketing bar 2 | 3

5 | 6 right bracketing bar + (-j^^) left bracketing bar 1 | 3

4 | 6 right bracketing bar + k^^ left bracketing bar 1 | 2

4 | 5 right bracketing bar

i^^ left bracketing bar 2 | 3

5 | 6 right bracketing bar = i^^ (2 6 - 3 5) = i^^ (-3) = -3 i^^:

-3 i^^ + (-j^^) left bracketing bar 1 | 3

4 | 6 right bracketing bar + k^^ left bracketing bar 1 | 2

4 | 5 right bracketing bar

-j^^ left bracketing bar 1 | 3

4 | 6 right bracketing bar = -j^^ (1 6 - 3 4) = -j^^ (-6) = 6 j^^:

-3 i^^ + 6 j^^ + k^^ left bracketing bar 1 | 2

4 | 5 right bracketing bar

k^^ left bracketing bar 1 | 2

4 | 5 right bracketing bar = k^^ (1 5 - 2 4) = k^^ (-3) = -3 k^^:

-3 i^^ + 6 j^^ - 3 k^^

-3 i^^ + 6 j^^ - 3 k^^ = (-3, 6, -3):

**Answer: | (-3, 6, -3)**

Guest Apr 6, 2017