A vector $a$ of magnitude 50 is collinear with the vector $6 i - 8 j - \frac{15}{2} k$ and making an obtuse angle with Z-axis is

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$24 i - 32 j - 30 k$

$- 24 i + 32 j + 30 k$

$24 i + 32 j - 30 k$

answer is A.

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Detailed Solution

$a = λ (6 i - 8 j - \frac{15}{2} k) |a| = |λ| \sqrt{36 + 64 + \frac{225}{4}} 50 = |λ| \frac{25}{2} \Rightarrow λ = \pm 4 given a . k < 0 a = 24 i - 32 j - 30 k$

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