Question 6 of 62

Passage question

00:00Est. 4 min

Marks+3.000.00

Passage

Let

T:\mathbb{R}^3\to\mathbb{R}^3

be a linear transformation defined by

T(x,y,z)=(x+y+z,\ x+2y+3z,\ 2x+3y+4z)

. Let

U=\{(x,y,z)\in\mathbb{R}^3\mid x+y+z=0\}

. Define the linear transformation

S=T|_U:U\to\mathbb{R}^3

. Based on the above data, answer the given subquestions.

Question

Consider a vector

v\in U

such that

S(v)\in\operatorname{span}\{(1,1,1)\}

, and

\|v\|^2=6

, where

\|\cdot\|

is the norm with respect to the standard inner product on

\mathbb{R}^3

. Which options are the possible choices for

v

ComprehensionMedium Difficulty06 April 2026