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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

  • Option 1)

    \pi \;

  • Option 2)

    \; 0\;

  • Option 3)

    \; \frac{\pi }{4}\;

  • Option 4)

    \; \frac{\pi }{2}

 

Answers (1)

best_answer

As we have learned

Collinear Vectors -

Two vectors are said to be collinear if and only if there exists a scalar m such as that \vec{a}=m\vec{b}

- wherein

m is a Scalar.

 

 

\vec{a}\cdot \vec{c} = 8 \vec{b} (-7 \vec{b }) \\= -56 |\vec{b}|^2 < 0

Also \vec{a}\: \: \: and \: \: \: \vec{b}  collinear where as \vec{b}\: \: \: and \: \: \: \vec{c}  collinear 

\Rightarrow \vec{a}\: \: \: and \: \: \: \vec{c}  collinear 

So , angle between  \vec{a}\: \: \: and \: \: \: \vec{c} = \pi

 

 

 


Option 1)

\pi \;

Option 2)

\; 0\;

Option 3)

\; \frac{\pi }{4}\;

Option 4)

\; \frac{\pi }{2}

Posted by

Himanshu

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