Question

Why are some of these scalars and others are vectors? What's the difference and how can you tell?

1. a dot (b x c)

2. (a dot b) x (b dot c)

3. (a + b) dot c

4. a x (b dot c)

5. (a x b) dot (b x c)

6. (a + b) x c

7. a dot (b dot c)

8. (a x b) + (b x c)

9. (a x b) - c

10. a x (b x c)

11. (a dot b) + (b dot c)

12. (a dot b) - c

I said that 1, 3, 5, and 11 are scalars. 6, 7, 8 and 9 are vectors. The rest are meaningless.

Answer 1

if <b>a</b> and <b>b</b> are vectors,

<b>a</b>•<b>b</b> is a scalar.
<b>a</b>×<b>b</b> is a vector.

the dot product • is only defined for two vectors.
The cross product × is only defined for two vectors.

So,
1,3,5,11 are scalars
6,8,9,10 are vectors
2,4,7,12 are undefined