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If  are three non-coplanar vectors, then

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Detailed Solution

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Concept:

If  are vectors, then

  • For dot product 
  • For cross product 

 

Calculation:

 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

⇒ 

∴ 

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Q1.If \(\rm\vec{a},\vec{b}\) and \(\rm\vec{c}\) are three non-coplanar vectors, then the value of \(\rm \frac{\vec{a}.(\vec{b}\times\vec{c})}{\vec{b}.(\vec{c}\times\vec{a})}+\rm \frac{\vec{b}.(\vec{c}\times\vec{a})}{\vec{c}.(\vec{a}\times\vec{b})}+\rm \frac{\vec{c}.(\vec{b}\times\vec{a})}{\vec{a}.(\vec{b}\times\vec{c})}\) is:
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Q6.Find the value of 'a' such that the vectors 2î - ĵ + k̂, î + 2ĵ - 3k̂ and 3î + aĵ + 5k̂ are coplanar.
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Q1.The vectors \(\rm \vec a, \vec b\ and\ \vec c\) are of the same length. If taken pairwise they form equal angles. If \(\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,\) then what can \(\vec c\) be equal to?  I. î + k̂  II. \(\rm \frac{-\hat i+4\hat j-\hat k}{3}\) Select the correct answer using the code given below. 
Q2.Let ABCDEF be a regular hexagon. If \(\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}\) then what is mn equal to 
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