Chapter 26 Multiple choice questions

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. What is the magnitude of the following vector: (4, 8, 1)?

13 correct incorrect

32 correct incorrect

11 correct incorrect

9 correct incorrect

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. Determine the following scalar multiplication:
$5\times \left(\begin{array}{c}2.1\\ 6.4\\ 7\end{array}\right)$.

$\left(\begin{array}{c}10.5\\ 32\\ 35\end{array}\right)$ correct incorrect

$\left(\begin{array}{c}10.5\\ 6.4\\ 7\end{array}\right)$ correct incorrect

$\left(\begin{array}{c}2.1\\ 32\\ 7\end{array}\right)$ correct incorrect

$\left(\begin{array}{c}2.1\\ 6.4\\ 35\end{array}\right)$ correct incorrect

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. If a = (4, 3, 9), b = (2, 8, 5), and c = (0, 7, 1), calculate the magnitude of 2a - 5b + 3c.

$\sqrt{141}$ correct incorrect

$3\sqrt{21}$ correct incorrect

$\sqrt{106}$ correct incorrect

$\sqrt{93}$ correct incorrect

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. If a = (2, 0, 9) and b = (4, -4, 6), calculate the relative motion of a ball moving with velocity vector a and the centre of a racquet, which is moving with velocity vector b.

(6, -4, 15) correct incorrect

(-6, 4, -15) correct incorrect

(2, -4, -3) correct incorrect

(-2, 4, 3) correct incorrect

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. Find the angle between $c=-3\widehat{i}+5\widehat{j}-8\widehat{k}$ and $d=-\widehat{i}+2\widehat{j}-4\widehat{k}$.

45° correct incorrect

21° correct incorrect

3.6° correct incorrect

7.3° correct incorrect

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. If $s=5\widehat{i}-6\widehat{j}-\widehat{k}$ and $t=2\widehat{i}+\widehat{j}-4\widehat{k}$, then find the cross-product $s\times t$.

$\left(\begin{array}{c}25\\ -18\\ 17\end{array}\right)$ correct incorrect

$\left(\begin{array}{c}25\\ 18\\ 17\end{array}\right)$ correct incorrect

$\left(\begin{array}{c}23\\ 22\\ -7\end{array}\right)$ correct incorrect

$\left(\begin{array}{c}23\\ -22\\ -7\end{array}\right)$ correct incorrect

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. Find the gradient of the field with equation: $E=4y^{3}z-3x^{4}y{z}^2+6z^3$ at the point (1, 4, 9).

$\nabla E=1485\widehat{i}+1498\widehat{j}-3888\widehat{k}$ correct incorrect

$\nabla E=1498\widehat{i}-3888\widehat{j}+1495\widehat{k}$ correct incorrect

$\nabla E=-3888\widehat{i}+1485\widehat{j}+1498\widehat{k}$ correct incorrect

$\nabla E=-3888\widehat{i}+1498\widehat{j}+1495\widehat{k}$ correct incorrect

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. Calculate the curl of the vector $M=3x^5{y}^{2}z\widehat{i}-6xyz\widehat{j}-2x^2{y}^4{z}^3\widehat{k}$ at the point (1, 3, 2).

$\nabla \times M=-1710\widehat{i}+2619\widehat{j}-72\widehat{k}$ correct incorrect

$\nabla \times M=27\widehat{i}-36\widehat{j}-648\widehat{k}$ correct incorrect

$\nabla \times M=-72\widehat{i}+2565\widehat{j}-1710\widehat{k}$ correct incorrect

$\nabla \times M=-2565\widehat{i}-72\widehat{j}-1710\widehat{k}$ correct incorrect

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. Calculate the divergence of the vector field $F=x^2{y}^3{z}^4\widehat{i}+5x{y}^{2}z\widehat{j}-3y^4{z}^5\widehat{k}$ at (2, 1, 5).

$\nabla \cdot F=-9375$ correct incorrect

$\nabla \cdot F=100$ correct incorrect

$\nabla \cdot F=2500$ correct incorrect

$\nabla \cdot F=-6775$ correct incorrect

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. Calculate the divergence of the vector field
$F=5r^3{e}_r+r^2\cos \theta e_{\theta }-r\sin \theta \cos \varphi e_{\varphi }$.

$\nabla \cdot F=25r^2+\frac{r{\cos }^2\theta }{\sin \theta }+\sin \varphi$ correct incorrect

$\nabla \cdot F=25r^2+\frac{r}{\sin \theta }\left({\cos }^2\theta -{\sin }^2\theta \right)$ correct incorrect

$\nabla \cdot F=25r^2+\frac{r\cos 2\theta }{\sin \theta }+\sin \varphi$ correct incorrect

$\nabla \cdot F=\frac{r}{\sin \theta }\left({\cos }^2\theta -{\sin }^2\theta \right)+\sin \varphi$ correct incorrect