If the vectors a-b-c-a-b-2c and -a-b-c are linearly dependent- then the value of - is

Given : nbsp;a+b+c,a+λb+2c and a+b+c. They are linearly dependent nbsp; ⇒ nbsp; 1 amp;1 amp;1 1 amp;λ amp;2 1 amp;1 amp;1 =0 ⇒ 1(λ 2) 1(1 ...

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Condition for Two Lines to be on the Same Plane

If the vector...

Question

If the vectors $\to a + \to b + \to c, \to a + λ \to b + 2 \to c$ and $- \to a + \to b + \to c$ are linearly dependent, then the value of $λ$ is

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\to a + 1343 \to b + \to c, - \to a + \to b + \to c

\to a + μ \to b + 2 \to c

μ =

\to a, \to b, \to c

λ

[λ (\to a + \to b) λ^{2} \to b λ \to c] = [\to a \to b + \to c \to b],

\to a, \to b, \to c

\to r

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

λ [\to a \to b \to c]

λ

\to a, \to b, \to c

\to r = \frac{(\to r . \to a) (\to b \times \to c) + (\to r . \to b) (\to c \times \to a) + (\to r . \to c) (\to a \times \to b)}{λ},

λ

\to a, \to b, \to c

λ

[λ (\to a + \to b), λ^{2} \to b, λ \to c] = [\to a, \to b + \to c, \to b]

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