Question Type 1: Finding the dot product between two vectors using different operations Bootcamps

Compute the dot product of the vectors $u=(3,0,4)$ and $v=(4,0,1)$.

Find the dot product of $u=(-2,5,3)$ and $v=(1,-4,2)$.

Given two vectors $u$ and $v$ satisfy $|u|=5$, $|v|=7$ and the angle between them is $60^\circ$, find $u\cdot v$.

Compute the dot product of the four-dimensional vectors $u=(1,2,3,4)$ and $v=(0,-1,2,-3)$.

Find the dot product of the five-dimensional vectors $u=(1,0,-2,3,1)$ and $v=(2,1,0,-1,4)$.

Determine the value of $\lambda$ such that the vectors $u=(1,\lambda,3)$ and $v=(2,-1,4)$ are perpendicular.

Let $u=(\cos\theta,\sin\theta)$ and $v=(1,1)$. Express $u\cdot v$ in terms of $\theta$.

Given $u=(2,1,0)$ and $v=(-1,3,4)$, compute the dot product of $u+v$ with $u-v$.

Let $u=(4,-2,1)$ and $v=(1,0,-1)$. Find the scalar projection of $u$ onto $v$.

Compute the dot product of the row vector from matrix $A$ and column vector $w$, where
$A=\begin{pmatrix}2 & -1 & 3\\0 & 4 & 1\\-2 & 5 & 0\end{pmatrix},\quad w=\begin{pmatrix}1\\2\\-1\end{pmatrix},$
and we take the first row of $A$.

Let $u(t)=(t,t^2,1)$ and $v(t)=(1,2t,t)$. Compute $u(2)\cdot v(2)$.