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Show that the Points A, B, C with Position Vectors `2hati- Hatj + Hatk`, `Hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` Respectively, Are the Vertices of a Right-angled Triangle. Hence Find the Area of the Triangle - CBSE (Science) Class 12 - Mathematics

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Question

Show that the points A, B, C with position vectors `2hati- hatj + hatk`, `hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle

Solution

Given

`veca =  2hati - hatj + hatk`

`vecb = hati -3hatj - 5hatk`

`vecc = 3hati - 4hatj - 4hatk`

then

`bar(AB) = vecb - veca`

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Solution Show that the Points A, B, C with Position Vectors `2hati- Hatj + Hatk`, `Hati - 3hatj - 5hatk` and `3hati - 4hatj - 4hatk` Respectively, Are the Vertices of a Right-angled Triangle. Hence Find the Area of the Triangle Concept: Introduction of Product of Two Vectors.
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