# arrow_back Is it possible to have $\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$ Explain.

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Is it possible to have $\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$ Explain.

If $\mathbf{n}=(a, b, c)$ is a unit vector, use this formula to show that (perhaps surprisingly) the orthogonal projection of $\mathbf{x}$ into the plane perpendicular to $\mathbf{n}$ is given bya) Let $\mathbf{v}:=(a, b, c)$ and $\mathbf{x}:=(x, y, z)$ be any vectors in $\mathbb{R}^{3}$. Viewed as column vectors, find a $3 \times 3$ m ...
Express the vector $\mathbf{u}=(2,3,1,2)$ in the form $\mathbf{u}=\mathbf{w}_{1}+\mathbf{w}_{2}$, where $\mathbf{w}_{1}$ is a scalar multiple of $\mathbf{a}=(-1,0,2,1)$ and $\mathbf{w}_{2}$ is orthogonal to a. Express the vector $\mathbf{u}=(2,3,1,2)$ in the form $\mathbf{u}=\mathbf{w}_{1}+\mathbf{w}_{2}$, where $\mathbf{w}_{1}$ is a scalar multiple of $\m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove the orthogonal projection theorem 1 answer 7 views Prove the orthogonal projection theoremProve the orthogonal projection theorem ... close 1 answer 8 views Find the orthogonal projections of the vectors$\mathbf{e}_{1}=(1,0)$and$\mathbf{e}_{2}=(0,1)$on the line$L$that makes an angle$\theta$with the positive$x$-axis in$R^{2}$.Find the orthogonal projections of the vectors$\mathbf{e}_{1}=(1,0)$and$\mathbf{e}_{2}=(0,1)$on the line$L$that makes an angle$\theta$with the ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the intercepts on the$x$- and$y$-axes (if any) for the function$f(x)=\frac{x^{2}-3}{x+2}$and discuss symmetry. 0 answers 7 views Find the intercepts on the$x$- and$y$-axes (if any) for the function$f(x)=\frac{x^{2}-3}{x+2}$and discuss symmetry.Find the intercepts on the$x$- and$y$-axes (if any) for the function$f(x)=\frac{x^{2}-3}{x+2}$and discuss symmetry. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$1 answer 7 views What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}\$ ...