# arrow_back Define a vector

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Define a vector

A vector is represented by a directed line segment. It has an initial point $A$ and a terminal point $B$. It has a length and a direction indicated by the arrow.

Note : A scalar has magnitude or size only, i.e., no direction, e.g. mass, speed, time, real number, ... In engineering, vectors are used for forces, velocity, weight, ...

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## Related questions

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 $\m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$1 answer 179 views What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$... close 0 answers 62 views 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 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$\mathbf{u}=(2,-1,3)$and$\mathbf{a}=(4,-1,2)$. Find the vector component of$\mathbf{u}$along a and the vector component of$\mathbf{u}$orthogonal to a. 1 answer 131 views Let$\mathbf{u}=(2,-1,3)$and$\mathbf{a}=(4,-1,2)$. Find the vector component of$\mathbf{u}$along a and the vector component of$\mathbf{u}$orthogonal to a.Let$\mathbf{u}=(2,-1,3)$and$\mathbf{a}=(4,-1,2)$. Find the vector component of$\mathbf{u}$along a and the vector component of$\mathbf{u}$orthog ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Is it possible to have$\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$Explain. 0 answers 102 views Is it possible to have$\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$Explain.Is it possible to have$\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$Explain. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Answer the following in terms of $\mathbf{V}, \mathbf{W}$, and $\mathbf{Z}$. 0 answers 76 views Answer the following in terms of $\mathbf{V}, \mathbf{W}$, and $\mathbf{Z}$.Let $A$ be a matrix, not necessarily square. Say $\mathbf{V}$ and $\mathbf{W}$ are particular solutions of the equations \(A \mathbf{V}=\mathbf{ ... close 0 answers 60 views Find an initial point$P$of a nonzero vector$\mathbf{u}=\overrightarrow{P Q}$with terminal point$Q(3,0,-5)$and such that$\mathbb{u}$has the same direction as$\mathbf{v}=(4,-2,-1)$.Find an initial point$P$of a nonzero vector$\mathbf{u}=\overrightarrow{P Q}$with terminal point$Q(3,0,-5)$and such that$\mathbb{u}$has the sam ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a terminal point$Q$of a nonzero vector$\mathbf{u}=\overrightarrow{P Q}$with initial point$P(-1,3,-5)$and such that 0 answers 58 views Find a terminal point$Q$of a nonzero vector$\mathbf{u}=\overrightarrow{P Q}$with initial point$P(-1,3,-5)$and such thatFind a terminal point$Q$of a nonzero vector$\mathbf{u}=\overrightarrow{P Q}$with initial point$P(-1,3,-5)$and such that (a)$\mathbf{u}$has 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 norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (2, 2, 2)$0 answers 57 views Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (2, 2, 2)$Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (2, 2, 2)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (1, -1, 2)$0 answers 88 views Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (1, -1, 2)$Find the norm of$v$, and a unit vector that is oppositely directed to$\mathbf{v} = (1, -1, 2)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a unit vector that is orthogonal to both$\mathbf{u}=(1,0,1)$and$\mathbf{v}=(0,1,1)$0 answers 188 views Find a unit vector that is orthogonal to both$\mathbf{u}=(1,0,1)$and$\mathbf{v}=(0,1,1)$Find a unit vector that is orthogonal to both$\mathbf{u}=(1,0,1)$and$\mathbf{v}=(0,1,1)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following is the unit vector in direction of$a \times b$if$a=(2,1,1)$and$b=(-1,2,2) ?$0 answers 50 views Which of the following is the unit vector in direction of$a \times b$if$a=(2,1,1)$and$b=(-1,2,2) ?$Which of the following is the unit vector in direction of$a \times b$if$a=(2,1,1)$and$b=(-1,2,2) ?$&nbsp; A.$\left(-\frac{1}{2}, \frac{1}{2}, ...
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You may choose the same option for matching more than once. Read through the following proof and match the lines with the reasons given below.
You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines $L 1$ to $L 5$.
You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines $L 1$ to $L 5$. You may choose the same option for matching more than once. Read through the following proof and spot an error or not in the lines $L 1$ to $L 5$. ...