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The position vector for an electron is v...

The position vector for an electron is `vecr=(6.0m)hati-(4.0m)hatj+(3.0m)hatk`. (a) Find the magnitude of `vecr`.

Text Solution

AI Generated Solution

To find the magnitude of the position vector \(\vec{r} = (6.0 \, \text{m}) \hat{i} - (4.0 \, \text{m}) \hat{j} + (3.0 \, \text{m}) \hat{k}\), we will follow these steps: ### Step 1: Identify the components of the vector The position vector \(\vec{r}\) has three components: - \(x\)-component: \(6.0 \, \text{m}\) (along \(\hat{i}\)) - \(y\)-component: \(-4.0 \, \text{m}\) (along \(\hat{j}\)) - \(z\)-component: \(3.0 \, \text{m}\) (along \(\hat{k}\)) ...
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Knowledge Check

  • For any vector vecr , ( vecr.hati) hati + ( vecr.hatj) hatj + ( vecr.hatk) hatk =

    A
    `vecr`
    B
    ` 2vecr`
    C
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    D
    `vec0`
  • If the point of intersection of the line vecr = (hati + 2 hatj + 3 hatk ) + ( 2 hati + hatj+ 2hatk ) and the plane vecr (2 hati - 6 hatj + 3 hatk) + 5=0 lies on the plane vec r ( hati + 75 hatj + 60 hatk) -alpha =0, then 19 alpha + 17 is equal to :

    A
    1555
    B
    1550
    C
    2563
    D
    2000
  • The position vectors of points A and B are hati - hatj + 3hatk and 3hati + 3hatj - hatk respectively. The equation of a plane is vecr cdot (5hati + 2hatj - 7hatk)= 0 The points A and B

    A
    Lie on the plane
    B
    Are on the same side of the plane
    C
    Are on the opposite sides of the plane
    D
    Nothing can be said
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