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Mathematics for Data Science II, Week-wise practice

Undated, Set week-01

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Question 1

+1−0Numerical answer

Let $u=(4, 1)$ and $v=(1, -2)$ . Find the dot product $u\cdot v$ .

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Let $u=(4, 1)$ and $v=(1, -2)$. Find the dot product $u\cdot v$. Let $u=(3, 0, 1)$ and $v=(-3, 2, -2)$. Find $\|u\|^2$, the square of the length of $u$. Let $u=(k, 1)$ and $v=(-1, -1)$. Find $k$ so that $u$ and $v$ are perpendicular (orthogonal).