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Values of the parameter for which Cxi - 6j - 3k and xi + 2j + 2Cxk make an obtuse angle for all x

The same question, asked 2 times: 2 May 2023 S1, 21 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    149
    For all real xx, the vectors Cxi^−6j^−3k^Cx\hat{i} - 6\hat{j} - 3\hat{k} and xi^+2j^+2Cxk^x\hat{i} + 2\hat{j} + 2Cx\hat{k} make an obtuse angle with each other, then the value of CC can be in

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  2. Question 2

    21 Apr 2025 S2

    124
    The value of m∈Rm\in\mathbb{R}, when angle between the vectors pˉ=myi^−6j^+3k^\bar{p}=my\widehat{i}- 6\widehat{j}+ 3\widehat{k} and qˉ=yi^+2j^+2myk^\bar{q}=y\widehat{i}+ 2\widehat{j}+ 2my\widehat{k} is obtuse angle, is

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