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Let |bar(a)|=7, |bar(b)|=11, | bar(a)+bar(b)|=10 sqrt(3) What is the angle between (bar(a)+bar(b) and (bar(a)-bar(b))? |
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Answer» `(pi)/(2)` `cos alpha = ((vec(a)+vec(b))(vec(a)-vec(b)))/(|vec(a)+vec(b)||vec(a)-vec(b)|)` `=((7)^(2)-(11)^(2))/(10sqrt(3)xx2sqrt(10))=((7+11)(7-11))/(20sqrt(3)xxsqrt(10))=(-18)/(5sqrt(30))` `=(-6xx3)/(5sqrt(30))xx(SQRT(30))/(sqrt(30))=-(3sqrt(30))/(25)` `alpha = cos ^(-1)((-3)/(5)sqrt((6)/(5)))` |
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