Let a→,b→ and c→ be three non-zero vectors such that b→ and c→ are non-collinear if a→+5b→ is collinear with c→,b→+6c→ is collinear with a→ and a→+αb→+βc→=0→, then α+β is equal to

a→+5b→=λc→ b→+6c→=μa→Eliminating a→λc→−5b→=6μc→+1μb→ μ=−15,λ=−30 α=5, β=30

Let a→,b→ and c→ be three non-zero vectors such that b→ and c→ are non-collinear if a→+5b→ is collinear with c→,b→+6c→ is collinear with a→ and a→+αb→+βc→=0→, then α+β is equal to

a→+5b→=λc→ b→+6c→=μa→Eliminating a→λc→−5b→=6μc→+1μb→ μ=−15,λ=−30 α=5, β=30

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear if $\vec{a} + 5 \vec{b}$ is collinear with $\vec{c}, \vec{b} + 6 \vec{c}$ is collinear with $\vec{a}$ and $\vec{a} + α \vec{b} + β \vec{c} = \vec{0}$ , then $α + β$ is equal to

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$\vec{a} + 5 \vec{b} = λ \vec{c} \vec{b} + 6 \vec{c} = μ \vec{a}$

Eliminating $\vec{a}$

$λ \vec{c} - 5 \vec{b} = \frac{6}{μ} \vec{c} + \frac{1}{μ} \vec{b} μ = \frac{- 1}{5}, λ = - 30 α = 5, β = 30$

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Let a→,b→ and c→ be three non-zero vectors such that b→ and c→ are non-collinear if a→+5b→ is collinear with c→,b→+6c→ is collinear with a→ and a→+αb→+βc→=0→, then α+β is equal to

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear if $\vec{a} + 5 \vec{b}$ is collinear with $\vec{c}, \vec{b} + 6 \vec{c}$ is collinear with $\vec{a}$ and $\vec{a} + α \vec{b} + β \vec{c} = \vec{0}$ , then $α + β$ is equal to