Answer to Question #226356 in Linear Algebra for Sarita bartwal

Question #226356
a. Find a unit vector in R^3 that is orthogonal to (1,2,1) and (1,-1,2).
b. If T: R^5 to R^3 is a linear transformation, then there is u
1
Expert's answer
2021-08-16T15:44:51-0400

"\\text{The vector orthogonal to both (1, 2, 1) and (1, -1, 2) is the vector cross}\n\\\\\\text{product between (1,2,1) and (1,-1,2)}\n\\\\\\begin{vmatrix}\n i & j & k\\\\\n 1 & 2 & 1 \\\\\n1 & -1 & 2\n\\end{vmatrix}\n\\\\=i\\begin{vmatrix}\n2 & 1\\\\\n-1 & 2\n\\end{vmatrix} -j\\begin{vmatrix}\n1 & 1\\\\\n1 & 2\n\\end{vmatrix} + k\\begin{vmatrix}\n1 & 2\\\\\n1 & -1\n\\end{vmatrix}=5i-j-3k\n\\\\\\text{The unit vector is}\n\\\\=\\frac{5i-j-3k}{\\sqrt{5^2+(-1)^2+(-3)^2}}=\\frac{5i-j-3k}{\\sqrt{35}}"


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