Question 15 of 43

Passage question

00:00Est. 2 min

Marks+1.000.00

Passage

Consider

u_1=\left(\frac1{\sqrt3},-\frac1{\sqrt3},\frac1{\sqrt3}\right)

u_2=\left(\frac1{\sqrt2},0,-\frac1{\sqrt2}\right)

, and

u_3=\left(\frac1{\sqrt6},\frac{2k}{\sqrt6},\frac{k}{\sqrt6}\right)

\mathbb{R}^3

, where

k\in\mathbb{R}

. Use the standard inner product to answer the subquestions.

Question

Find the value of

k

for which

\{u_1,u_2,u_3\}

is an orthonormal basis of

\mathbb{R}^3

ComprehensionMedium Difficulty01 December 2024

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