Question

Consider vector a in the positive direction of x, vector b in the positive direction of y, and scalar d. What is the direction of vector b/d if d is positive and negative? What is the magnitude of (a dot b) and (a dot b/d)? What is the direction of the vector resulting from (a cross b) and (b cross a)? What are the magnitudes of these cross products? What are the magnitudes and the direction of (a cross b/d) if d is positive?

Answer 1

if d is positive, then, b/d is a positive vector the same direction with b
if d is negative, then b/d is a vector opposite way with b and the magnitude = b/d

Answer 2

\(a \bullet b\)

Answer 3

Why is the magnitude b/d and not sqrt of the components?

Answer 4

a =<a, 0> and b =<0, b> they are perpendicular, so, \(a\bullet b =0\)

Answer 5

I am sorry, I thought you know it. because since we talk about magnitude, we have to calculate the magnitude of the vector, right? so, I thought no need to confirm it

Answer 6

Yeah and the magnitude of the vector is equal to \[\sqrt{components of the vector}\]

Answer 7

now a x b . you can use the formula a x b = \(| {\vec a}|*|\vec b|*sin \dfrac{\pi}{2}\)

Answer 8

the same if we calculate a x (b/d)

Answer 9

What is the magnitude of (a dot b) and (a dot b/d)? What is the direction of the vector resulting from (a cross b) and (b cross a)? What are the magnitudes of these cross products? What are the magnitudes and the direction of (a cross b/d) if d is positive?

Answer 10

0
because they are perpendicular.

Answer 11

Please tell me which question you are referring to. There are many. There are other questions I need help with as well. Please respond to all.

Answer 12

The dot product depends upon the angle of the vectors. One formula for the dot product is:
\[v \dot u = ||v||*||u|| cos(\theta)\]
Where theta is the angle between them, so if the angle is 90 degrees, the dot produt is always zero. This means the vectors are "orthogonal" or independent of each other and can form a basis.

Answer 13

Ok and the cross product is with sin so wouldn't that be 1 if theta is 90 degrees?

Answer 14

Yes, but also be aware that the cross product always returns a vector, that direction of the vector is orthogonal to both vectors, so this means its coming "out of the page"

Answer 15

Oh ok. Last thing. What is the direction of the vector resulting from (a cross b) and (b cross a)? What are the magnitudes and the direction of (a cross b/d) if d is positive?

Answer 16

Hello?
Please! I need your help.

Answer 17

!!!!!!!!!!!!!!!!