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The points with position vectors

\vec{3i}-\vec{4j}-\vec{4k}, \vec{2i}-\vec{j}+\vec{k}\: and\: \vec{i}-\vec{3j}-\vec{5k}

  • Option 1)

    An Equilateral Triangle

  • Option 2)

    An Isosceles Triangle

  • Option 3)

    A Right Angle Triangle

  • Option 4)

    None of these

 

Answers (1)

best_answer

As we learnt

Scalar Product of two vectors -

\vec{a}.\vec{b}> 0 \:an\: acute\: angle

\vec{a}.\vec{b}< 0 \:an\: obtuse\: angle

\vec{a}.\vec{b}= 0 \:a\:right\: angle

- wherein

\Theta  is the angle between the vectors \vec{a}\:and\:\vec{b}

 

 \vec{A}=3i-4j-4k

\vec{B}=2i-j+k

\vec{C}=i-3j-5k

\underset{AB}{\rightarrow}= -i+3j+5k

\underset{AC}{\rightarrow}= -2i+j-k

\underset{AB}{\rightarrow}.\underset{AC}{\rightarrow}=2+3-5=0

So that it is right angle triangle


Option 1)

An Equilateral Triangle

Incorrect option

Option 2)

An Isosceles Triangle

Incorrect option

Option 3)

A Right Angle Triangle

Correct option

Option 4)

None of these

Incorrect option

Posted by

Plabita

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