If vec a and vec b are parallel vectors, then [vec a,vec c,vec b] is equal to (1) 2 (2) -1 (3) 1 (4) 0

Exercise 6.10 · Q1

\vec a

(1)

2

(2)

-1

(3)

1

(4)

0

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✓ Free question

Whenever two of the three vectors entering a scalar triple product are parallel, the resulting "parallelepiped" is flat (zero height), so its volume — and hence the scalar triple product — is always $0$ .

Step 1. Recall the coplanarity/degeneracy link. $[\vec x,\vec y,\vec z]=0$ whenever $\vec x,\vec y,\vec z$ are coplanar; in particular, if any two of the three are parallel, the three automatically lie in a common plane (spanned by that shared direction and the third vector).

Step 2. Apply to $[\vec a,\vec c,\vec b]$ . Here $\vec a\parallel\vec b$ is given — two of the three vectors ( $\vec a$ and $\vec b$ ) are parallel, regardless of what $\vec c$ is.

Step 3. Conclude. $[\vec a,\vec c,\vec b]=0$ , matching option (4).

✓Final answer

[\vec a,\vec c,\vec b]=\boxed{0}

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Q.If $\vec a$ and $\vec b$ are parallel vectors, then $[\vec a,\vec c,\vec b]$ is equal to

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