Question

- If a and b are parallel vectors,then [ á,c,b] is equal to ​

Answer 1

$[\vec{a}\:\vec{c}\:\vec{b}]=0$

Tips:

We know that, if $\vec{a}$ and $\vec{b}$ be two parallel vectors, then

$\vec{a}\times\vec{b}=\vec{0}$

Also, $[\vec{a}\:\vec{b}\:\vec{c}]=[\vec{b}\:\vec{c}\:\vec{a}]=[\vec{c}\:\vec{a}\:\vec{b}]$

Here, $[\vec{a}\:\vec{b}\:\vec{c}]=\vec{a}.(\vec{b}\times\vec{c})$

Step-by-step explanation:

We know that, if $\vec{a}$ and $\vec{b}$ be two parallel vectors, then

$\vec{a}\times\vec{b}=\vec{0}$

Now, $[\vec{a}\:\vec{c}\:\vec{b}]$

$=[\vec{c}\:\vec{b}\:\vec{a}]$

$=\vec{c}.(\vec{b}\times\vec{a})$

$=\vec{c}.(-\vec{a}\times\vec{b})$

• since $\vec{a}\times\vec{b}=-\vec{b}\times\vec{a}$

$=\vec{c}.(-\vec{0})$

• since $\vec{a}\times\vec{b}=\vec{0}$

$=-\vec{c}.\vec{0}$

$=0$

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