In a right-handed Cartesian coordinate system | vedclass

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Question

(A) In a right-handed Cartesian coordinate system,the unit vectors $\hat{i}, \hat{j}, 	ext{ and } \hat{k}$ follow the cyclic order: $\hat{i} 	imes \

Vedclass · Accepted Answer

$\hat{j} 	imes \hat{k} = \hat{i}$

Vedclass · Answer

(A) In a right-handed Cartesian coordinate system,the unit vectors $\hat{i}, \hat{j}, 	ext{ and } \hat{k}$ follow the cyclic order: $\hat{i} 	imes \hat{j} = \hat{k}$,$\hat{j} 	imes \hat{k} = \hat{i}$,and $\hat{k} 	imes \hat{i} = \hat{j}$. Option $(A)$ is correct because $\hat{j} 	imes \hat{k} = \hat{i}$. Option $(B)$ is incorrect because the dot product of orthogonal unit vectors is zero $(\hat{k} \cdot \hat{i} = 0)$. Option $(C)$ is incorrect because the dot product of a unit vector with itself is one $(\hat{i} \cdot \hat{i} = 1)$. Option $(D)$ is incorrect because the cross product of a vector with itself is the zero vector $(\hat{j} 	imes \hat{j} = \vec{0})$.

Column $I$	Column $II$
$(A) (A+B)$	$(p)$ North-east
$(B) (A-B)$	$(q)$ Vertically upwards
$(C) (A \times B)$	$(r)$ Vertically downwards
$(D) (A \times B) \times (A \times B)$	$(s)$ None

In a right-handed Cartesian coordinate system (often referred to as a clockwise system when viewed from the positive axis),which of the following vector relations is correct?

Similar Questions

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Column $I$ Column $II$

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$(C) (A \times B)$ $(r)$ Vertically downwards

$(D) (A \times B) \times (A \times B)$ $(s)$ None

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