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Value of lambda making a + lambda b perpendicular to c

This type of question, asked 5 times: 2 May 2023 S1, 10 May 2023 S2, 16 May 2023 S2, 10 May 2024 S1, 11 May 2024 S2. All 5 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    124
    If a⃗=(2i^+2j^+3k^)\vec{a} = (2\hat{i} + 2\hat{j} + 3\hat{k}), b⃗=(−i^+2j^+k^)\vec{b} = (-\hat{i} + 2\hat{j} + \hat{k}) and c⃗=(3i^+j^)\vec{c} = (3\hat{i} + \hat{j}) such that (a⃗+λb⃗)(\vec{a} + \lambda\vec{b}) is perpendicular to c⃗\vec{c}, then the value of λ\lambda is

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  2. Question 2

    10 May 2023 S2

    141
    If a⃗=2i^+2j^+3k^\vec{a} = 2\hat{i}+2\hat{j}+3\hat{k}, b⃗=−i^+2j^+k^\vec{b} = -\hat{i}+2\hat{j}+\hat{k} and c⃗=3i^+j^\vec{c} = 3\hat{i}+\hat{j} such that b⃗+λa⃗\vec{b}+\lambda\vec{a} is perpendicular to c⃗\vec{c}, then λ\lambda is

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  3. Question 3

    16 May 2023 S2

    131
    If a⃗=2i^+2j^+3k^\vec{a} = 2\hat{i}+2\hat{j}+3\hat{k}, b⃗=−i^+2j^+k^\vec{b} = -\hat{i}+2\hat{j}+\hat{k} and c⃗=3i^+j^\vec{c} = 3\hat{i}+\hat{j} are vectors such that a⃗+λb⃗\vec{a}+\lambda\vec{b} is perpendicular to c⃗\vec{c}, then value of λ\lambda is

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  4. Question 4

    10 May 2024 S1

    109
    If a⃗=2i^+3j^+2k^\vec{a}=2\hat{i}+3\hat{j}+2\hat{k}, b⃗=2i^+j^\vec{b}=2\hat{i}+\hat{j} and c⃗=i^+3j^\vec{c}=\hat{i}+3\hat{j} are such that a⃗+λb⃗\vec{a}+\lambda\vec{b} is perpendicular to c⃗\vec{c}, then the value of λ\lambda is

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  5. Question 5

    11 May 2024 S2

    145
    If a⃗=2i^+3j^+2k^\vec{a}=2\hat{i}+3\hat{j}+2\hat{k}, b⃗=2i^+j^−k^\vec{b}=2\hat{i}+\hat{j}-\hat{k} and c⃗=3i^−j^\vec{c}=3\hat{i}-\hat{j} are such that a⃗+λb⃗\vec{a}+\lambda\vec{b} is perpendicular to c⃗\vec{c}, then the value of λ\lambda is

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