Question

(2j×3i).k=? My text book says the answer is -6. But how?

Answer 1

See below

Explanation:

`2 hat j times 3 hat i = 2times 3 (hat j times hat i) = 6(-hat i times hat j) = -6 hat k`

Thus

`(2 hat j times 3 hat i )cdot hat k = -6\ hat k cdot hat k = -6`

Here we have used the following properties

• `vec A times vec B = -vec B times vec A`
• `hat i times hat j = hat k`
• `hat k cdot hat k = |hat k|^2=1`

You could of course also use the determinant form for the scalar triple product

`(2 hat j times 3 hat i )cdot hat k = hat k cdot (2 hat j times 3 hat i )`
`qquadqquad qquad qquadqquad quad = |(0,0,1),(0,2,0),(3,0,0)|=-6`
but this will be an overkill for this problem.