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The position vectors of the vertices of ...

The position vectors of the vertices of `DeltaABC` are `3 hat i - 4 hat j - 4 hat k`, `2 hat i - hat j + hat k` and `hat i - 3 hat j - 5 hat k` respectively.
(i) Find `vec (AB),` `vec(BC)` and `vec(CA)`.
(ii) Prove that `DeltaABC` is a right angled triangle.
(iii) Find the unit vector perpendicular to both ` vec (AB)` and `vec(BC)`.

Text Solution

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The correct Answer is:
(i) `2 hat i - hat j + hat k`
(ii) `therefore vec(AB) bot vec(CA)` Hence `DeltaABC` is a right angled triangle.
(iii) `(1)/(sqrt 210) (-8 hat i - 11 hat j + 5 hat k)`
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