The values of a- for which the points A-B-C with position vectors 2-k-3-5k- and a-3-k- respectively are the vertices of a right angled triangle with C- -2 are

Show that the points A,B and C with position vectors, $a = 3^i - 4^j - 4^k, b = 2^i -^j +^k a n d c =^i - 3^j - 5^k$ respectively, form the vertices of a right angled triangle.

Q. Show that the points

A, B, C

with position vectors

2^i -^j +^k,^i - 3^j - 5^k

and

3^i - 4^j - 4^k

respectively, are the vertices of a right-angled triangle. Hence, find the area of the triangle.

Show that the points A,B,C with position vectors $2^i -^j +^k,^i - 3^j - 5^k,$ and $3^i - 4^j - 4^k$ respectively,are the vertices of a right-angled triangle. Hence find the area of the rectangle.

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The values of a, for which the points A,B,C with position vectors 2^i−^j+^k,^i−3^j−5^k and a^i−3^j+^k respectively are the vertices of a right angled triangle with C=π2 are

The correct option is C 2 and 1→BC.→AC=0⇒((a−2)^i−2^j).((a−1)^i+4^k)=0Therefore, (a−2)(a−1)=0⇒a=2,1

The values of a, for which the points A,B,C with position vectors $2^i -^j +^k,^i - 3^j - 5^k$ and $a^i - 3^j +^k$ respectively are the vertices of a right angled triangle with C= $\frac{π}{2}$ are

The correct option is C $2$ and $1$
$\to B C . \to A C = 0$

$\Rightarrow ((a - 2)^i - 2^j) . ((a - 1)^i + 4^k) = 0$

Therefore, $(a - 2) (a - 1) = 0$

$\Rightarrow a = 2, 1$