91影视

This problem is based on the product rule in which the vector product and scalar product are the two ways of multiplying vectors. To construct the scalar product, one multiplies the magnitude of the component of one vector by the magnitude of the component of the other vector. Similarly, When two vectors are multiplied by the sine of the angle between them, the magnitude of the vector product can be found.

Consider, eastward is $\hat{\mathrm{i}}$, northward is $\hat{\mathrm{j}}$, and upward is $\hat{\mathrm{k}}$respectively.

Using the fundamental product rule $\hat{\mathrm{i}},\hat{\mathrm{j}},\hat{\mathrm{k}}$can be written as

$\hat{\mathrm{i}}脳\hat{\mathrm{j}}=-\hat{\mathrm{j}}脳\mathrm{i}=\hat{\mathrm{k}}$ (i)

role="math" localid="1656308707958" $\hat{\mathrm{j}}脳\hat{\mathrm{k}}=-\hat{\mathrm{k}}脳\hat{\mathrm{j}}=\hat{\mathrm{i}}$ (ii) $\hat{\mathrm{k}}脳\hat{\mathrm{i}}=-\hat{\mathrm{i}}脳\hat{\mathrm{k}}=\hat{\mathrm{j}}$ (iii)

eastward is $\hat{\mathrm{i}}$, so west is $-\hat{\mathrm{i}}$therefore,

$\hat{\mathrm{j}}脳-\hat{\mathrm{i}}=\hat{\mathrm{k}}=\mathrm{up}$

Similarly,

$(-\hat{\mathrm{k}})路(-\hat{\mathrm{j}})=0$

$\hat{\mathrm{i}}脳\hat{\mathrm{k}}=-\hat{\mathrm{j}}\mathrm{south}\hat{\mathrm{i}}$

$(-\hat{\mathrm{i}})鈰�(-\hat{\mathrm{i}})=1$

$(-\hat{\mathrm{j}})鈰�(-\hat{\mathrm{j}})=1$