What is the value of $(A$ $(A$ x $B)^{2}$ $B)^2$ + ${(A \cdot B)}^{2}$ $(A * B)^2$ ?

Question

What is the value of $(A$ $(A$ x $B)^{2}$ $B)^2$ + ${(A \cdot B)}^{2}$ $(A * B)^2$ ?

Please interpret this as the sum of the squares of the cross product and dot product of two vectors A and B.
Thanks:)

1 Answer

Impact of this question

65683 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-29T13:37:47

${| A |}^{2} {| B |}^{2}$ $absA^2 absB^2$

Explanation:

$| A \times B | = | A | | B | sin ϕ$ $abs(A xx B)=absA absB sinphi$
$| A \cdot B | = | A | | B | cos ϕ$ $abs(A cdot B)=absA absB cos phi$

here $ϕ$ $phi$ is the angle between $A$ $A$ and $B$ $B$ at common tails.

then

${| A \times B |}^{2} + {| A \cdot B |}^{2} = {| A |}^{2} {| B |}^{2} ({sin}^{2} ϕ + {cos}^{ϕ}) = {| A |}^{2} {| B |}^{2}$ $abs(A xx B)^2+abs(A cdot B)^2=absA^2absB^2(sin^2phi+cos^phi) = absA^2absB^2$

Science

Math

Humanities

... and beyond

What is the value of $(A$ $(A$ x $B)^{2}$ $B)^2$ + ${(A \cdot B)}^{2}$ $(A * B)^2$ ?

Please interpret this as the sum of the squares of the cross product and dot product of two vectors A and B.
Thanks:)

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the value of (A(A xB)2 B)^2 + (A⋅B)2(A * B)^2 ?

Please interpret this as the sum of the squares of the cross product and dot product of two vectors A and B. Thanks:)

1 Answer

Explanation:

Related questions

Impact of this question

What is the value of $(A$ $(A$ x $B)^{2}$ $B)^2$ + ${(A \cdot B)}^{2}$ $(A * B)^2$ ?

Please interpret this as the sum of the squares of the cross product and dot product of two vectors A and B.
Thanks:)