If a and b are unit vectors, and |a+b|=root3, determine (2a-5b)*(b+3b). (JUST ASSUME " * " STANDS FOR THE DOT)
I've gotten part of the question, where a*b=1/2, and i've gotten up to: 2a*b - 5b*3a + 6a*a - 5b*b for the other equation. I know a*a and b*b are going to be replaced with 1 eventually. I'm just stuck with evaluating the rest of the equation, so I can substitute a*b=1/2 in it. Thanks for the help!
I've gotten part of the question, where a*b=1/2, and i've gotten up to: 2a*b - 5b*3a + 6a*a - 5b*b for the other equation. I know a*a and b*b are going to be replaced with 1 eventually. I'm just stuck with evaluating the rest of the equation, so I can substitute a*b=1/2 in it. Thanks for the help!
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Is (2a-5b)*(b+3b) supposed to be (2a−5b) • (b+3a) or (2a−5b) • (a+3b) ?
From your result, I assume the first one
Since a and b are unit vectors, then
a•a = |a|² = 1² = 1
b•b = |b|² = 1² = 1
|a+b| = √3
|a+b|² = 3
a•a + 2a•b + b•b = 3
1 + 2a•b + 1 = 3
2a•b = 1
a•b = 1/2
(2a−5b) • (b+3a)
= 2a•b + 6a•a − 5b•b − 15b•a
= 1 + 6 − 5 − 15/2
= −11/2
From your result, I assume the first one
Since a and b are unit vectors, then
a•a = |a|² = 1² = 1
b•b = |b|² = 1² = 1
|a+b| = √3
|a+b|² = 3
a•a + 2a•b + b•b = 3
1 + 2a•b + 1 = 3
2a•b = 1
a•b = 1/2
(2a−5b) • (b+3a)
= 2a•b + 6a•a − 5b•b − 15b•a
= 1 + 6 − 5 − 15/2
= −11/2