Q49 / 105 · JEE Main 2008 · Mathematics

The non-zero verctors $\vec{a}, \vec{b}$ and $\vec{c}$ are related by $\vec{a}=8 \vec{b}$ and $\vec{c}=-7 \vec{b}$. Then the angle between $\vec{a}$ and $\overrightarrow{\mathrm{c}}$ is

  • A
    0
  • B
    $\pi / 4$
  • C
    $\pi / 2$
  • Correct answer
    D
    $\pi$

Solution

Since $\vec{a}=8 \vec{b}$ $$ \overrightarrow{\mathrm{c}}=-7 \overrightarrow{\mathrm{b}} $$ $\therefore \vec{a}$ and $\vec{b}$ are like vectors and $\vec{b}$ and $\vec{c}$ are unlike. $\Rightarrow \vec{a}$ and $\vec{c}$ will be unlike Hence, angle between $\vec{a}$ and $\vec{c}=\pi$.

Hence, the correct answer is option: 'D'.

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