Answer to Question #342847 in Analytic Geometry for guy

Question #342847

Let vector A=a1i +a2j + a3k and B=b1i + b2j + b3k ne on the same plane. Fine the unit vector perpendicular to both A and B.


1
Expert's answer
2022-05-22T23:46:57-0400
"A\\times B=\\begin{vmatrix}\n \\vec{i} & \\vec{j} & \\vec{k} \\\\\n a_1 & a_2 & a_3 \\\\\n b_1 & b_2 & b_3\n\\end{vmatrix}"

"=(a_2b_3-a_3 b_2)\\vec{i}+(a_3b_1-a_1b_3)\\vec{j}+(a_1b_2-a_2b_1)\\vec{k}"

"\\vec {u}=\\langle\\dfrac{a_2b_3-a_3 b_2}{\\sqrt{(a_2b_3-a_3 b_2)^2+(a_3b_1-a_1 b_3)^2+(a_1b_2-a_2 b_1)^2}},"


"\\dfrac{a_3b_1-a_1b_3}{\\sqrt{(a_2b_3-a_3 b_2)^2+(a_3b_1-a_1 b_3)^2+(a_1b_2-a_2 b_1)^2}},"

"\\dfrac{a_1b_2-a_2b_1}{\\sqrt{(a_2b_3-a_3 b_2)^2+(a_3b_1-a_1 b_3)^2+(a_1b_2-a_2 b_1)^2}}\\rangle"


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