Yahoo Answers: Answers and Comments for Math Homework Help Vectors Grade 12? [Mathematics]
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From Valeria
enCA
Tue, 23 Jul 2019 02:34:36 +0000
3
Yahoo Answers: Answers and Comments for Math Homework Help Vectors Grade 12? [Mathematics]
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https://ca.answers.yahoo.com/question/index?qid=20190723023436AAi0zQO
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From ted s: 1)....you know that W dot S =  W  S  cos &...
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https://ca.answers.yahoo.com/question/index?qid=20190723023436AAi0zQO
Tue, 23 Jul 2019 03:39:11 +0000
1)....you know that W dot S =  W  S  cos <(W,S)....and scalar projection of W on S is  W  cos <(W , S )....
let W = 3 A + 4 B & S = B......( 3 A + 4 B ) dot( B ) = 3 ( A dot B) + 4  B ²....
projection is { 3  A   B  cos < (A,B)+ 4  B ² } /  B  = 3 (2) ( 1 / 2) + 4 (4) =13

From az_lender: (1) will be easier if we take a specific case....
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https://ca.answers.yahoo.com/question/index?qid=20190723023436AAi0zQO
Tue, 23 Jul 2019 03:32:30 +0000
(1) will be easier if we take a specific case. Let B = 4i, and then A could be i+j*sqrt(3). Then 3A + 4B would be 13i + 3j*sqrt(3). The projection of the latter vector onto B is simply its projection on the xaxis, which has scalar magnitude 13.
(2) If the vector projection of S on R is (2,1,7), then R has the same direction as (2,1,7).
Formally, (2,1,7) = (S "dot" R/ R)(R / R).The quantity in the last parentheses is the unit vector in the direction (2,1,7), which would be (2,1,7)/sqrt(54).
Therefore, sqrt(54) = (S "dot" R)/ R, and
R sqrt(54) = R S cos(110) =>
S = sqrt(54)/cos(110).
As the cos(110) is negative, I guess I can use the negative square root of 54, and get
S = 11.603... .
And so R = 23.206...
and R = (23.206)*(2,1,7)/sqrt(54)
= 3.158*(2,1,7) = (6.316,3.158, 22 point something, use calculator)