If the projection of the vector $\hat{i} + 2 \hat{j} + \hat{k}$ on the sum of the two vectors $2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $- λ \hat{i} + 2 \hat{j} + 3 \hat{k}$ is 1, then $λ$ is equal to_________.

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alok kumar singh | Contributor-Level 10

2 months ago

$\vec{a} = \hat{i} + 2 \hat{j} + \hat{k}$

$\vec{b} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k} \vec{c} = - λ \hat{i} + 2 \hat{j} + 3 \hat{k}$

$\vec{b} + \vec{c} = (2 - λ) \hat{i} + 6 \hat{j} - 2 \hat{k}$

${(12 - λ)}^{2} = {(2 - λ)}^{2} + 40$

$λ = 5$

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If the projection of the vector $\hat{i} + 2 \hat{j} + \hat{k}$ on the sum of the two vectors $2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $- λ \hat{i} + 2 \hat{j} + 3 \hat{k}$ is 1, then $λ$ is equal to_________.

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If the projection of the vector i ^ + 2 j ^ + k ^ on the sum of the two vectors 2 i ^ + 4 j ^ − 5 k ^ and − λ i ^ + 2 j ^ + 3 k ^ is 1, then λ is equal to_________.

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If the projection of the vector $\hat{i} + 2 \hat{j} + \hat{k}$ on the sum of the two vectors $2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $- λ \hat{i} + 2 \hat{j} + 3 \hat{k}$ is 1, then $λ$ is equal to_________.