If r-x-y-zk- find r-r- j - xy-

r⃗ =xî +yĵ +zk̂ ⇒r⃗×î = yk̂ +zĵ ⇒r⃗×ĵ =xk̂ zî ⇒ (r⃗×î ).(r⃗×ĵ )=( yk̂ +zĵ ).(xk̂ zî )= xy ⇒ (r⃗×î ).(r⃗×ĵ )+xy=0 ...

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Expression Formation

If r=xî+yĵ+...

Question

If $\to r = x^i + y^j + z^k$ , find $(\to r \times^i) . (\to r \times j) + x y .$

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Solution

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r = x^i + y^j + z^k

(\to r \times^i) (\to r \times^j) + x y

^i \times ((^a -^j) \times^i) +^j \times ((^a -^k) \times^j) +^k \times ((^a -^i) \times^k) = \to 0

\to a = x^i + y^j + z^k,

8 (x^{3} - x y + z x)

\to r = x^i + y^j + z^k

{\to a}_{1} = x^i -^j +^k

{\to a}_{2} =^i + y^j + 2^k

x^i + y^j + z^k

¯ a = x^i - 2^j + 5^k

¯ b =^i + y^j - z^k

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