If a- -2b- -3c- -0 and a-b- -b-c- -c-a-is equal to - b-c- then - is equal to

The correct option is D None of theseGiven a⃗+2b⃗+3c⃗=0 i.e., a⃗= 2b⃗ 3c⃗ Now a⃗×b⃗+b⃗×c⃗+c⃗×a⃗=λ(b⃗×c⃗) i.e., ( 2b⃗ 3c⃗)×b⃗+b⃗×c⃗+c⃗×( 2b⃗ 3c ...

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Applications of Dot Product

If a⃗ +2b⃗ ...

Question

If $\to a + 2 \to b + 3 \to c = 0$ and $\to a \times \to b + \to b \times \to c + \to c \times \to a$ is equal to $λ (\to b \times \to c)$ then $λ$ is equal to

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Solution

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\to a + 2 \to b + 3 \to c = 0

\to b \times \to c + \to c \times \to a + \to a \times \to b

(\to b \times \to c) \times (\to c \times \to a) = 3 \to c

[\to b \times \to c

\to c \times \to a

\to a \times \to b] =

[\to a \to b \to c] = 4

\to a \times \to b = \to c, \to b \times \to c = 2 \to a

\to c \times \to a = λ \to b,

λ

| \to a | = 3, ∣ ∣ \to b ∣ ∣ = 4, | \to c | = 5, \to a ⊥ (\to b + \to c), \to b ⊥ (\to c + \to a)

\to c ⊥ (\to a + \to b)

\sqrt{2} ∣ ∣ \to a + \to b + \to c ∣ ∣

\to a, \to b

\to c

\to b + \to c, \to c + \to a

\to a + \to b

| \to a + \to b | = 6, | \to b + \to c | = 8

| \to c + \to a | = 10

| \to a + \to b + \to c |

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