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2. Vectors u and v are given by: u=5i-4j+ pk v=2i+tj-3k (a) Express p in terms of t when u and v are perpendicular. ​

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If u and v are perpendicular, then their dot product is zero:

[tex]\vec u \cdot \vec v = (5\,\vec\imath-4\,\vec\jmath+p\,\vec k) \cdot (2\,\vec\imath+t\,\vec\jmath - 3\,\vec k) = 10 - 4t - 3p = 0[/tex]

Solve for p :

[tex]10 - 4t - 3p = 0[/tex]

[tex]3p = 10 - 4t[/tex]

[tex]\boxed{p = \dfrac{10-4t}3}[/tex]
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