[amp_mcq option1=”\\[\\sqrt {48} \\]” option2=”\\[\\sqrt {56} \\]” option3=”\\[\\sqrt {24} \\]” option4=”\\[\\sqrt {12} \\]” correct=”option4″]<\/p>\n
The correct answer is $\\boxed{\\sqrt{24}}$.<\/p>\n
The Euclidean norm (also called the 2-norm, L2 norm, or Euclidean distance) of a vector $v$ is defined as:<\/p>\n
$$\\|v\\|2 = \\sqrt{v^Tv} = \\sqrt{\\sum<\/em>{i=1}^n v_i^2}$$<\/p>\n where $v_i$ is the $i$th element of $v$ and $n$ is the number of elements in $v$.<\/p>\n In this case, $v = [4 -2 -6]^T$, so:<\/p>\n $$\\|v\\|_2 = \\sqrt{4^2 + (-2)^2 + (-6)^2} = \\sqrt{40} = \\sqrt{2^3\\cdot5} = 2\\sqrt{2}\\sqrt{5} = \\sqrt{24}$$<\/p>\n Option A is incorrect because $\\sqrt{48} = 2\\sqrt{24}$. Option B is incorrect because $\\sqrt{56} = 2\\sqrt{28}$. Option C is incorrect because $\\sqrt{24} \\neq \\sqrt{12}$.<\/p>\n","protected":false},"excerpt":{"rendered":" [amp_mcq option1=”\\[\\sqrt {48} \\]” option2=”\\[\\sqrt {56} \\]” option3=”\\[\\sqrt {24} \\]” option4=”\\[\\sqrt {12} \\]” correct=”option4″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20215","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\n