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

The correct option is C 2 and 1 A⃗C⃗=(α 2)î 2ĵ B⃗C⃗=(α 1)î A⃗C⃗⊥B⃗C⃗ A⃗C⃗.B⃗C⃗=0 (α 2)(α 1)=0 α =2,1 ...

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Standard XII

Mathematics

Applications of Dot Product

The value of ...

Question

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

- 2

and

1

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2

and

- 1

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2

and

1

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- 2

and

- 1

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Solution

The correct option is C $2$ and $1$
$\to A C = (α - 2)^i - 2^j$
$\to B C = (α - 1)^i$
$\to A C ⊥ \to B C$
$\to A C . \to B C = 0$
$(α - 2) (α - 1) = 0$
$α = 2, 1$

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

The correct option is C 2 and 1→AC=(α−2)^i−2^j→BC=(α−1)^i→AC⊥→BC→AC.→BC=0(α−2)(α−1)=0α=2,1

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

The correct option is C $2$ and $1$
$\to A C = (α - 2)^i - 2^j$
$\to B C = (α - 1)^i$
$\to A C ⊥ \to B C$
$\to A C . \to B C = 0$
$(α - 2) (α - 1) = 0$
$α = 2, 1$