Operations with Vectors
Read this topicExplanations 3
- Operations with Vectors Addition Given v⃗=⟨v1,v2⟩\vec{v}= \langle \color{#8925AE}{v_1},\color{#8925AE}{v_2} \ranglev=⟨v1,v2⟩ and let u⃗=⟨u1,u2⟩\vec{u}= \langle \color{#29A603}…
By Alex Federspiel, Moor Xu, Eunji Kwon, Anusha Rahman
- (Video) Vector Operations by Math and Stats Help This video by Math and Stats Help reviews the basic operations that we can do with vectors. Operations on Vectors Given u=<2,3>u…
By Anusha Rahman
- Operations with Vectors There are four main operations that we can do with vectors. Looking Further Vector-valued functions provide another way of parametrizing a curve by expre…
By Anusha Rahman
Problems 16
- Let x⃗,y⃗\vec{x}, \vec{y}x,y be column vectors of length 333 and z⃗\vec{z}z be a row vector of length 333. Let AAA be an 3×33\times 33×3 matrix. Which of the following are vali…
- Given v⃗=⟨8,10⟩\vec{v}=\langle 8,10 \ranglev=⟨8,10⟩ and u⃗=⟨4,3⟩\vec{u}=\langle 4,3 \rangleu=⟨4,3⟩, find v⃗+u⃗\vec{v}+\vec{u}v+u.
- Given v⃗=⟨8,10⟩\vec{v}=\langle 8,10 \ranglev=⟨8,10⟩ and u⃗=⟨4,3⟩\vec{u}=\langle 4,3 \rangleu=⟨4,3⟩, find v⃗−u⃗\vec{v}-\vec{u}v−u.
- Given v⃗=⟨8,10⟩\vec{v}= \langle 8,10 \ranglev=⟨8,10⟩ and u⃗=⟨4,3⟩\vec{u}= \langle 4,3 \rangleu=⟨4,3⟩, find ∥v⃗+u⃗∥\Vert \vec{v}+\vec{u} \Vert∥v+u∥.
- Given v⃗=⟨8,10⟩\vec{v}=\langle 8,10 \ranglev=⟨8,10⟩ and c=13c=13c=13, find cv⃗c\vec{v}cv.
- Given v⃗=⟨13,0,7⟩\vec{v}= \langle 13,0,7 \ranglev=⟨13,0,7⟩, u⃗=⟨12,10,15⟩\vec{u}= \langle 12,10,15 \rangleu=⟨12,10,15⟩, and w⃗=⟨13,3,9⟩\vec{w}= \langle 13,3,9 \ranglew=⟨13,3,9⟩,…
- Given v⃗=⟨13,0,7⟩\vec{v} = \langle 13,0,7 \ranglev=⟨13,0,7⟩, u⃗=⟨12,10,15⟩\vec{u}= \langle 12,10,15 \rangleu=⟨12,10,15⟩, and w⃗=⟨13,3,9⟩\vec{w}= \langle 13,3,9 \ranglew=⟨13,3,9⟩…
- Let v⃗=⟨2,2,3⟩\vec{v}= \langle 2, 2, 3 \ranglev=⟨2,2,3⟩ and w⃗=⟨1,−1,1⟩\vec{w}= \langle 1, -1, 1 \ranglew=⟨1,−1,1⟩. Calculate v⃗−w⃗\vec{v} - \vec{w}v−w.
- Given v⃗=⟨4,1,−2⟩\vec{v}= \langle 4, 1, -2 \ranglev=⟨4,1,−2⟩ and c=4c= 4c=4, solve for cv⃗c\vec{v}cv.
- Let v⃗=⟨−1,2,−3⟩\vec{v}= \langle -1, 2, -3 \ranglev=⟨−1,2,−3⟩, w⃗=⟨0,3,2⟩\vec{w}= \langle 0, 3, 2\ranglew=⟨0,3,2⟩, and c=2c=2c=2. Calculate c(v⃗+w⃗)c (\vec{v}+ \vec{w})c(v+w).
- Let v⃗=⟨−5,11,3⟩\vec{v}= \langle -5, 11, 3 \ranglev=⟨−5,11,3⟩ and w⃗=⟨1,0,6⟩\vec{w}= \langle 1, 0, 6 \ranglew=⟨1,0,6⟩. Calculate v⃗+w⃗\vec{v} + \vec{w}v+w.
- Let v⃗=⟨5,1,3⟩\vec{v}= \langle 5, 1, 3 \ranglev=⟨5,1,3⟩. Solve for ∥v⃗∥\lVert \vec{v} \rVert∥v∥.
- Let v⃗=⟨2,2⟩\vec{v}= \langle 2, 2 \ranglev=⟨2,2⟩, u⃗=⟨8,5⟩\vec{u}= \langle 8, 5 \rangleu=⟨8,5⟩, and w⃗=⟨−1,−4⟩\vec{w}= \langle -1, -4 \ranglew=⟨−1,−4⟩. Calculate u⃗+(v⃗−w⃗)\vec{…
- Let v⃗=⟨19,0,7⟩\vec{v}= \langle 19, 0, 7 \ranglev=⟨19,0,7⟩ and w⃗=⟨1,3,6⟩\vec{w}= \langle 1, 3, 6 \ranglew=⟨1,3,6⟩. Calculate v⃗−w⃗\vec{v} - \vec{w}v−w.
- Given v⃗=⟨0,11,4⟩\vec{v}= \langle 0, 11, 4\ranglev=⟨0,11,4⟩ and c=−1c= -1c=−1, solve for cv⃗c\vec{v}cv.
- Given v⃗=⟨−2,6,3⟩\vec{v}= \langle -2, 6, 3\ranglev=⟨−2,6,3⟩ and c=−3c= -3c=−3, solve for cv⃗c\vec{v}cv.