Find the vector p- which is perpendicular to both a-4-5-k- and b-4-5k- and p-q-21 and q-3-k-

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Applications of Cross Product

Find the vect...

Question

Find the vector $\to p$ which is perpendicular to both $\to a = 4^i + 5^j -^k$ and $\to b =^i - 4^j + 5^k$ and $\to p \cdot \to q = 21$ and $\to q = 3^i +^j -^k$ .

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\to a = 4^i + 5^j -^k, \to b =^i - 4^j + 5^k, and \to c = 3^i -^j -^k

\to d

\to c

\to b

\to d

\to a = 21

\to r

\to a =^i - 2^j + 5^k

\to b = 2^i + 3^j -^k

\to r . (2^i +^j +^k) + 8 = 0

\to a =^i + 4^j + 2^k, \to b = 3^i - 2^j + 7^k

\to c = 2^i -^j + 4^k

\to p

\to a

\to b

\to p \cdot \to c = 18.

\to a = 3^i + 4^j - 5^k

|^i \times (\to a \times^i) +^j \times (\to a \times^j) +^k \times (\to a \times^k) | =

\to A =^i + 4^j - 2^k

\to B = 3^i - 5^j +^k

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