Consider R^2 with standard inner product. If u = beginpmatrixabendpmatrix is the vector in R^2 such that the inner product of u with beginpmatrix12endpmatrix is 2 and with beginpmatrix4-2endpmatrix is -1, then which one of the following statements is true?

(D) Inner product of u with beginpmatrix-1/21endpmatrix is 4/5

Q15Section ST (Statistics (Q11–Q65))15 of 65

Inner products fixing a vector

Consider $\mathbb{R}^2$ with standard inner product. If $\mathbf{u} = \begin{pmatrix}a\\b\end{pmatrix}$ is the vector in $\mathbb{R}^2$ such that the inner product of $\mathbf{u}$ with $\begin{pmatrix}1\\2\end{pmatrix}$ is 2 and with $\begin{pmatrix}4\\-2\end{pmatrix}$ is $-1$ , then which one of the following statements is true?

Pick an option to check your answer. In a mock test a wrong answer here costs 1/3 mark.

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