Question

Homework-2: Problem 15 (1 point) Let ( vec{a}, vec{b}, vec{c} ) and ( vec{y} ) be the three dimensional vectors [ vec{a}=vec{j}+5 vec{k}, quad vec{b}=-2 vec{i}+8 vec{j}+3 vec{k}, quad vec{c}=4 vec{i}+5 vec{j}, quad vec{y}=-vec{i}+8 vec{j} ] Perform the following operations on these vectors: (a) ( vec{c} cdot vec{a}+vec{a} cdot vec{y}= ) (b) ( (vec{a} cdot vec{b}) vec{a}= ) (c) ( ((vec{c} cdot vec{c}) vec{a}) cdot vec{a}= )

          Homework-2: Problem 15
(1 point)
Let ( vec{a}, vec{b}, vec{c} ) and ( vec{y} ) be the three dimensional vectors
[
vec{a}=vec{j}+5 vec{k}, quad vec{b}=-2 vec{i}+8 vec{j}+3 vec{k}, quad vec{c}=4 vec{i}+5 vec{j}, quad vec{y}=-vec{i}+8 vec{j}
]
Perform the following operations on these vectors:
(a) ( vec{c} cdot vec{a}+vec{a} cdot vec{y}= )
(b) ( (vec{a} cdot vec{b}) vec{a}= )
(c) ( ((vec{c} cdot vec{c}) vec{a}) cdot vec{a}= )

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Homework-2: Problem 15
(1 point)
Let ( veca, vecb, vecc ) and ( vecy ) be the three dimensional vectors
[
veca=vecj+5 veck, quad vecb=-2 veci+8 vecj+3 veck, quad vecc=4 veci+5 vecj, quad vecy=-veci+8 vecj
]
Perform the following operations on these vectors:
(a) ( vecc cdot veca+veca cdot vecy= )
(b) ( (veca cdot vecb) veca= )
(c) ( ((vecc cdot vecc) veca) cdot veca= )

Added by Elif Ç.

Linear Algebra and Its Applications

David C. Lay, Steven R. Lay, Judi J.… 5th Edition

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Transcript

00:01 Alright, so let's rewrite a, b, c, and y into the component form.

00:04 So for a, this is going to equal 0, 1, 5.

00:09 For b, that's going to equal negative 2, 8, 3.

00:14 For c, that's going to be 4, 5, 0.

00:17 And lastly, for y, that's going to be negative 1, 8, 0.

00:24 So for letter a, we need to take the dot product of c and a and add that to the dot product of a and y.

00:29 So the dot product between c and a is just going to be 4, 5, 0, dot, 0, 1, 5.

00:38 So we're going to take 4 and multiply it by 0 and add it to 5 times 1 and then add 0 times 5.

00:48 So that's going to equal 5.

00:51 And then for the dot product between a and y, that's going to be 0, 1, 5, dot, with negative 1, 8, 0.

00:59 So that equals 0 times negative 1 plus 1 times 8 plus 5 times 0, which ends up being equal to 8.

01:10 So then this is just going to be 5 plus 8, which equals 13.

01:16 Next we need to find the dot product between a and b.

01:21 So that is going to be 0, 1, 5, dot, with negative 2, 8, 3.

01:27 So that just equals 0 times negative 2 plus 1 times 8 plus 5 times 3.

01:35 So that is going to equal 8 plus 15, which is 23.

01:41 So then we need to take 23 and multiply that by 0, 1, 5...

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