If $A = < 2, 1, 6 >$ $A = <2 ,1 ,6 >$ , $B = < 5, 1, 7 >$ $B = <5 ,1 ,7 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

Question

If $A = < 2, 1, 6 >$ $A = <2 ,1 ,6 >$ , $B = < 5, 1, 7 >$ $B = <5 ,1 ,7 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

1 Answer

Impact of this question

1428 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-11T11:11:59

$α ≅ 17^{o}$ $alpha~=17^o$

Explanation:

$A = < 2, 1, 6 > \Rightarrow | | A | | = \sqrt{2^{2} + 1^{2} + 6^{2}} = \sqrt{41}$ $A= <2,1,6> => ||A||=sqrt(2^2+1^2+6^2)=sqrt41$
$B = < 5, 1, 7 > \Rightarrow | | B | | = \sqrt{5^{2} + 1^{2} + 7^{2}} = \sqrt{75}$ $B= <5,1,7> =>||B||=sqrt(5^2+1^2+7^2)=sqrt75$
$find A.B$ $"find A.B"$
$A . B = A_{x} \cdot B_{x} + A_{y} \cdot B_{y} + A_{z} \cdot B_{z}$ $A.B=A_x*B_x+A_y*B_y+A_z*B_z$
$A . B = 2 \cdot 5 + 1 \cdot 1 + 6 \cdot 7 A . B = 10 + 1 + 42 = 53$ $A.B=2*5+1*1+6*7" "A.B=10+1+42=53$
$A \cdot B is determined by :$ $A*B" is determined by :"$
$A \cdot B = | | A | | \cdot | | B | | \cdot cos α$ $A*B=||A||*||B||*cos alpha$
$53 = \sqrt{41} \cdot \sqrt{76} \cdot cos α$ $53=sqrt41*sqrt76*cos alpha$
$53 = \sqrt{41 \cdot 75} \cdot cos α$ $53=sqrt(41*75)*cos alpha$
$cos α = \frac{53}{\sqrt{3075}}$ $cos alpha=53/sqrt3075$
$cos α = \frac{53}{55, 45}$ $cos alpha=53/(55,45)$
$cos α = 0, 955816$ $cos alpha=0,955816$
$α ≅ 17^{o}$ $alpha~=17^o$

Science

Math

Humanities

... and beyond

If $A = < 2, 1, 6 >$ $A = <2 ,1 ,6 >$ , $B = < 5, 1, 7 >$ $B = <5 ,1 ,7 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If A = <2 ,1 ,6 >A=<2,1,6>A = <2 ,1 ,6 >, B = <5 ,1 ,7 >B=<5,1,7>B = <5 ,1 ,7 > and C=A-BC=A−BC=A-B, what is the angle between A and C?

1 Answer

Explanation:

Related questions

Impact of this question

If $A = < 2, 1, 6 >$ $A = <2 ,1 ,6 >$ , $B = < 5, 1, 7 >$ $B = <5 ,1 ,7 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?