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Scalar product of i + j + k with the unit vector along the sum of 2i + 4j - 5k and lambda i + 2j + 3k is 1: find lambda

The same question, asked 2 times: 9 May 2024 S1, 17 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    9 May 2024 S1

    101
    The scalar product of the vector i^+j^+k^\hat{i}+\hat{j}+\hat{k} with a unit vector along the sum of the vectors 2i^+4j^−5k^2\hat{i}+4\hat{j}-5\hat{k} and λi^+2j^+3k^\lambda\hat{i}+2\hat{j}+3\hat{k} is equal to 1, then value of λ\lambda is

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  2. Question 2

    17 Apr 2026 S2

    89
    The value of bb such that the scalar product of the vector i^+j^+k^\hat{i} + \hat{j} + \hat{k} with the unit vector parallel to the sum of the vectors 2i^+4j^−5k^2\hat{i} + 4\hat{j} - 5\hat{k} and bi^+2j^+3k^b\hat{i} + 2\hat{j} + 3\hat{k} is one, is...

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