Let a- b- c- be vectors of length 3- 4 and 5 respectively- Let a- be perpendicular to b- - c- b- to c- - a- and c- to a- - b- Find the length of the vector a- - b- - c-

Given, |a⃗|=3, |b⃗|=4, |c⃗|=5 Again a⃗⊥ (b⃗+c⃗) a⃗.(b⃗+c⃗)=0 #160; #160; ....(1) b⃗⊥ (c⃗+a⃗) b⃗.(c⃗+a⃗)=0 #160; #160; ....(2 ...

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Applications of Cross Product

Let a⃗, b⃗,...

Question

Let $\to a, \to b, \to c$ be vectors of length $3, 4$ and $5$ respectively. Let $\to a$ be perpendicular to $(\to b + \to c), \to b$ to $(\to c + \to a)$ and $\to c$ to $(\to a + \to b)$ . Find the length of the vector $\to a + \to b + \to c$ .

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\to a, \to b

\to c

\to p, \to q

\to r

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(\to a + \to b) \cdot \to p + (\to b + \to c) \cdot \to q + (\to c + \to a) \cdot \to r =

\to a, \to b, \to c

1, 1

2

\to a \times (\to a \times \to c) + \to b = \to 0

\to a

\to c

\to a, \to b

\to c

\to a + \to b + \to c = \to 0

| \to a | = 3, | \to b = 5

| \to c | = 7

\to a

\to b .

\to a, \to b, \to c

\to a \neq 0

\to a \times \to b = 2 \to a \times \to c, | \to a | = | \to c | = 1, | \to b | = 4

| \to b \times \to c | = \sqrt{15}

\to b - 2 \to c = λ \to a

λ

\to a

\to b

\to c

\to c = \to a + \to b

(\to a \times \to b) . (\to b \times \to c) + (\to b \times \to c) . (\to c \times \to a) + (\to c \times \to a) . (\to a \times \to b)

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