Find the projection of vector a -2- -3- -2k- on a vector b - -2- -k-

The vector projection of a⃗ on b⃗ is given by =a⃗.b⃗|b⃗| =(2i+3j+2k).(i+2j+k)√(1+2^2+1^2) =10√(6) ...

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Applications of Dot Product

Find the proj...

Question

Find the projection of vector $\to a = 2^i + 3^j + 2^k$ on a vector $\to b =^i + 2^j +^k$

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Solution

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2^i + 3^j - 2^k

^i + 2^j - 3^k

The given vectors can form sides of a triangle $^i -^j -^k, - 2^i + 3^j -^k,^i - 2^j + 2^k$

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

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

\to a =^i - 3^k, . \to b = 2^j -^k, \to c = 2^i - 3^j + 2^k

2^i -^j +^k

^i - 2^j +^k .

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