find the magnitude of u cross v and the unit vector parallel to u cross v in the direction of u cross v u=2i+2j-k, v=-i+k

Question

find the magnitude of u cross v and the unit vector parallel to u cross v in the direction of u cross v u=2i+2j-k, v=-i+k

in progress 0
RuslanHeatt 4 years 2021-07-22T05:32:00+00:00 1 Answers 19 views 0

Answers ( )

  1. thuhuong
    0
    2021-07-22T05:33:33+00:00
    Reply

    Recall that

    \|\mathbf u\times\mathbf v\|=\|\mathbf u\|\|\mathbf v\|\sin\theta

    where \theta is the angle between the vectors \mathbf u and \mathbf v. No need to actually compute the cross product.

    We can find the angle between the vectors using the dot product formula,

    \mathbf u\cdot\mathbf v=\|\mathbf u\|\|\mathbf v\|\cos\theta

    \implies\theta=\cos^{-1}\left(\dfrac{(2\mathbf i+2\mathbf j-\mathbf k)\cdot(-\mathbf i+\mathbf k)}{\sqrt{2^2+2^2+(-1)^2}\sqrt{(-1)^2+1^2}}\right)=\cos^{-1}\left(-\dfrac1{3\sqrt2}\right)

    Then

    \|\mathbf u\times\mathbf v\|=3\sqrt2\sin\theta=\boxed{\sqrt{17}}

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )