Given a→, b→ and c→ are 3 vectors such that b→,c→ are parallel unit vectors and a→=3. If a→+λc→=4b→, then the sum of all the possible positive values…

Question

Given a→, b→ and c→ are 3 vectors such that b→,c→ are parallel unit vectors and a→=3. If a→+λc→=4b→, then the sum of all the possible positive values of λ is

MARKS Content Team · Accepted Answer

Correct answer: 8. a→=4b→-λc→ a→|^2=16b→^2+λ^2c→^2-8λb→.c→ 9=16+λ^2-8λb→.c→ ⇒λ^2-8λ+7=0 as b→⋅c→=1 Sum of all the values of λ=8

Given $\vec{a}, \vec{b}$ and $\vec{c}$ are $3$ vectors such that $\vec{b}, \vec{c}$ are parallel unit vectors and $|\vec{a}| = 3$ . If $\vec{a} + λ \vec{c} = 4 \vec{b}$ , then the sum of all the possible positive values of $λ$ is

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