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Unit Vectors

Find P⃗ . Q...

Question

Find $\to P . \to Q$
where $\to P = 2^i +^j +^k$ and $\to Q =^i -^j + 2^k$

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Solution

$\to P . \to Q = (2^i +^j +^k) .^i -^j + 2^k) = 2 - 1 + 2 = 3$

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\to P =^i + 2^k

\to Q = 2^i +^j - 2^k

are two vectors, find the unit vector parallel to

\to P \times \to Q

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Q. Find a vector

\to r

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

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Q. Find the shortest distance between the lines.

\to r =^i + 2^j +^k + λ (^i -^j +^k)

\to r = 2^i -^j -^k + μ (2^i +^j + 2^k)

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