If vec{A}=3 hat{i}-2 hat{j}+hat{k},vec{B}=hat | vedclass

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(B) First,calculate the magnitudes squared of the vectors:$A^2 = |\vec{A}|^2 = 3^2 + (-2)^2 + 1^2 = 9 + 4 + 1 = 14$$B^2 = |\vec{B}|^2 = 1^2 + (-3)^2 +

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$\vec{A}=\vec{B}+\vec{C}$ and $B^2=A^2+C^2$

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(B) First,calculate the magnitudes squared of the vectors:$A^2 = |\vec{A}|^2 = 3^2 + (-2)^2 + 1^2 = 9 + 4 + 1 = 14$$B^2 = |\vec{B}|^2 = 1^2 + (-3)^2 + 5^2 = 1 + 9 + 25 = 35$$C^2 = |\vec{C}|^2 = 2^2 + 1^2 + (-4)^2 = 4 + 1 + 16 = 21$We observe that $B^2 = A^2 + C^2$ $(35 = 14 + 21)$,which satisfies the Pythagorean theorem for a right-angled triangle.Next,check the vector sum relation:$\vec{A} + \vec{C} = (3+2)\hat{i} + (-2+1)\hat{j} + (1-4)\hat{k} = 5\hat{i} - \hat{j} - 3\hat{k} 
eq \vec{B}$$\vec{B} = \vec{A} + \vec{C}$ is not satisfied. Let us check $\vec{A} = \vec{B} + \vec{C}$:$\vec{B} + \vec{C} = (1+2)\hat{i} + (-3+1)\hat{j} + (5-4)\hat{k} = 3\hat{i} - 2\hat{j} + \hat{k} = \vec{A}$Thus,$\vec{A} = \vec{B} + \vec{C}$ and $B^2 = A^2 + C^2$ is the correct condition.

Column-$I$	Column-$II$
$(1)$ Resultant of two vectors is maximum	$(a)$ $180^o$
$(2)$ Resultant of two vectors is minimum	$(b)$ $90^o$
	$(c)$ $0^o$

Column $-I$	Column $-II$
$(a) \vec a + \vec b = \vec c$	$(i)$ Vector $\vec a$ is along $+Y$,$\vec c$ is along $+X$,and $\vec b$ connects the origin to the tip of $\vec c$
$(b) \vec a - \vec c = \vec b$	$(ii)$ Vector $\vec a$ is along $+X$,$\vec b$ is along $+Y$,and $\vec c$ connects the origin to the tip of $\vec b$
$(c) \vec b - \vec a = \vec c$	$(iii)$ Vector $\vec c$ is along $+X$,$\vec a$ is along $+Y$,and $\vec b$ connects the tip of $\vec c$ to the tip of $\vec a$
$(d) \vec a + \vec b + \vec c = 0$	$(iv)$ Vector $\vec a$ is along $-X$,$\vec b$ is along $-Y$,and $\vec c$ connects the origin to the tip of $\vec b$

If $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}$,$\vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=2 \hat{i}+\hat{j}-4 \hat{k}$ form a right-angled triangle,then which of the following is satisfied?

Similar Questions

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Resultant of two vectors is maximum $(a)$ $180^o$

$(2)$ Resultant of two vectors is minimum $(b)$ $90^o$

$(c)$ $0^o$

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A} + \vec{B} = \vec{A} - \vec{B}$. Then:

What displacement must be added to the displacement $25\hat{i} - 6\hat{j} \text{ m}$ to give a resultant displacement of $7.0 \text{ m}$ pointing in the $X$-direction?

There are two force vectors,one of $5\, N$ and the other of $12\, N$. At what angle should the two vectors be added to get a resultant vector of $17\, N$,$7\, N$,and $13\, N$ respectively?

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