If a-b- b-c-0- with a- -c- then show that a-c- k b- where k is scalar-

a⃗×b⃗= b⃗×c⃗ a⃗×b⃗= c⃗×b⃗ ∴a⃗×b⃗= c⃗×b⃗= 0 ( a⃗+c⃗ )×b⃗= 0 ∴a⃗×b⃗≠ 0, b⃗×c⃗≠ 0, a⃗, b⃗, c⃗ are non zero vectors. #160; ( a⃗+c⃗ ...

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Multiplication with Vectors

If a⃗×b⃗= b...

Question

If $\to a \times \to b = \to b \times \to c \neq \to 0 w i t h \to a \neq - \to c$ then show that $\to a + \to c = k \to b,$ where k is scalar.

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Solution

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\to a \times \to b = \to b \times \to c \neq 0

\to a + \to c = m \to b

m

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

\to a \times \to b = \to b \times \to c = \to c \times \to a

\to a, \to b, \to c

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

| \to a | = | \to b | = | \to c |

\to a, \to b, \to c

\to a, \to b, \to c

\to a \times \to b = \to b \times \to c = \to c \times \to a

[\to a \to b \to c] = 0.

\to a, \to b, \to c

\to a . \to b = \to a . \to c, \to a \times \to b = \to a \times \to c, \to a \neq 0

\to b = \to c

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