The non-zero vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} =…

The non-zero vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$. Then the angle between $\vec{a}$ and $\vec{c}$ is
  1. $\pi$
  2. 0    
  3. π4    
  4. π2

Solution

$\vec{a} = 8\vec{b}$ $\vec{c} = -7\vec{b}$ $\vec{a}$ and $\vec{b}$ are parallel and $\vec{b}$ and $\vec{c}$ are antiparallel. Thus $\vec{a}$ and $\vec{c}$ are antiparallel. Hence the angle between $\vec{a}$ and $\vec{c}$ is $\pi$.

Asked in: MHT CET Full Test 3

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