If a- - -a- - - - -a- - - - -k- - then find the unit vector a-

Let a⃗=xî+yĵ+zk̂, a⃗.î=a⃗.(î+ĵ)=a⃗.(î+ĵ+k̂) x=x+y=x+y+z y=0,z=0 ∵a⃗ is a unit vector x=1a⃗=î ...

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Applications of Dot Product

If a⃗ .î =a...

Question

If $\to a .^i = \to a . (^i +^j) = \to a . (^i +^j +^k),$ then find the unit vector $\to a .$

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Solution

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\to a .^i = 4

(\to a \times^j) . (2^j - 3^k) =

\to A = 4^i + 2^j + 6^k

\to A .^i

\to A .^j

\to A .^k

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

\to B =^i +^j +^k

If $\to a = 4^i -^j +^k$ and $\to b = 2^i - 2^j +^k,$ then find a unit vector parallel to the vector $\to a + \to b$ .

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

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

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

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

(\to a \times \to b) \times (\to c \times \to d)

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