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Unknown component from perpendicular or parallel vectors

This type of question, asked 7 times: 23 Apr 2025 S1, 13 Apr 2026 S2, 16 Apr 2026 S2, 17 Apr 2026 S2, 20 Apr 2026 S2, 12 May 2026 S1, 13 May 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    23 Apr 2025 S1

    46
    If P→=bi^+6j^+k^\overrightarrow{P}=b\widehat{i}+ 6\widehat{j}+\widehat{k} and Q→=i^−aj^+4k^\overrightarrow{Q}=\widehat{i}-a\widehat{j}+ 4\widehat{k} are perpendicular to each other, also 3b−a=53b-a= 5. The value of aa and bb is

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  2. Question 2

    13 Apr 2026 S2

    102
    Calculate the values of aa and bb if vectors ai^+bj^=n^a\hat{i} + b\hat{j} = \hat{n} and (i^+j^)(\hat{i} + \hat{j}) are perpendicular to each other

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  3. Question 3

    16 Apr 2026 S2

    102
    Vectors ai^+bj^+k^a\hat{i} + b\hat{j} + \hat{k} and 2i^−3j^+4k^2\hat{i} - 3\hat{j} + 4\hat{k} are perpendicular to each other when 3a+2b=73a + 2b = 7, the ratio of a to b is x/2x/2. The value of x is

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  4. Question 4

    17 Apr 2026 S2

    101
    There are two vectors A⃗=6i^+9j^−k^\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k} and B⃗=2i^+3j^−pk^\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k} which have the same direction. The value of 'p' is

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  5. Question 5

    20 Apr 2026 S2

    102
    If two vectors A⃗=4i^+nj^+2k^\vec{A} = 4\hat{i} + n\hat{j} + 2\hat{k} and B⃗=2i^+2j^−k^\vec{B} = 2\hat{i} + 2\hat{j} - \hat{k} are mutually perpendicular to each other then value of 'n' is

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  6. Question 6

    12 May 2026 S1

    101
    If A⃗=5i^+2j^\vec{A} = 5\hat{i} + 2\hat{j} and B⃗=ai^+3j^\vec{B} = a\hat{i} + 3\hat{j} are perpendicular to each other, the value of 'a' is

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  7. Question 7

    13 May 2026 S2

    101
    The vector P⃗=ai^+aj^+3k^\vec{P} = a\hat{i} + a\hat{j} + 3\hat{k} and Q⃗=ai^−2j^−k^\vec{Q} = a\hat{i} - 2\hat{j} - \hat{k} are perpendicular to each other. Then positive value of 'aa' is

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