Show that the vectors 2i- -j- -k- i- -3j- -5k- and -3i- -4j- -4k- are the sides of a right angled triangle-

Let a⃗ =2i⃗ j⃗ +k⃗ , b⃗ =i⃗ 3j⃗ 5k⃗ and #160; c⃗ = 3i⃗ +4j⃗ +4k⃗ We see that a⃗ +b⃗ +c⃗ =0 ∴a⃗ ,b⃗ ,c⃗ forms a triangle #160;fur ...

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Applications of Dot Product

Show that the...

Question

Show that the vectors $2 \to i - \to j + \to k$ , $\to i - 3 \to j - 5 \to k$ and $- 3 \to i + 4 \to j + 4 \to k$ are the sides of a right angled triangle.

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4 \to i - 3 \to j + \to k, 2 \to i - 4 \to j + 5 \to k, \to i - \to j

A, B

C

2 \to i - \to j + \to k, \to i - 3 \to j - 5 \to k

3 \to i - 4 \to j - 4 \to k

{cos}^{2} A

\to r = 3 \to i + 2 \to j - 5 \to k

\to a = 2 \to i - \to j + \to k

\to b = \to i + 3 \to j - 2 \to k

\to c = - 2 \to i + \to j - 3 \to k

\to r = λ \to a + μ \to b + ν \to c

\to r = (\to i + 2 \to j - 5 \to k) + t (2 \to i - 3 \to j + 4 \to k)

\to r \cdot (2 \to i + 4 \to j - \to k) = 3

{\to F}_{1} = 3 \to i - 4 \to j + 2 \to k, {\to F}_{2} = 2 \to i + 3 \to j - \to k, {\to F}_{3} = 2 \to i + 4 \to j - 5 \to k

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