Let $$\overset{\to }{\mathop{p}}\,,\overset{\to }{\mathop{q}}\,,\overset{\to }{\mathop{r}}\,$$ be three mutually perpendicular vectors of the same magnitude. If a vector $$\vec{x}$$ satisfies the equation $$\overset{\to }{\mathop{p}}\,\times \{(\overset{\to }{\mathop{x}}\,-\overset{\to }{\mathop{q}}\,)\times \overset{\to }{\mathop{p}}\,\}+\overset{\to }{\mathop{q}}\,\times \{(\overset{\to }{\mathop{x}}\,-\overset{\to }{\mathop{r}}\,))\times \overset{\to }{\mathop{q}}\,\}$$$$+\overset{\to }{\mathop{r}}\,\times \{(\overset{\to }{\mathop{x}}\,-\overset{\to }{\mathop{p}}\,)\times \overset{\to }{\mathop{r}}\,\}=\overset{\to }{\mathop{0}}\,$$ then $$\overset{\to }{\mathop{x}}\,$$ is given by

Question

TuteeHUB · Accepted Answer

$$\frac{1}{3}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,+\overset{\to }{\mathop{r}}\,)$$

TuteeHUB · Answer

$$\frac{1}{2}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,-2\overset{\to }{\mathop{r}}\,)$$

TuteeHUB · Answer

$$\frac{1}{2}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,+\overset{\to }{\mathop{r}}\,)$$

TuteeHUB · Answer

$$\frac{1}{3}(2\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,-\overset{\to }{\mathop{r}}\,)$$

1.	Let \[\overset{\to }{\mathop{p}}\,,\overset{\to }{\mathop{q}}\,,\overset{\to }{\mathop{r}}\,\] be three mutually perpendicular vectors of the same magnitude. If a vector \[\vec{x}\] satisfies the equation \[\overset{\to }{\mathop{p}}\,\times \{(\overset{\to }{\mathop{x}}\,-\overset{\to }{\mathop{q}}\,)\times \overset{\to }{\mathop{p}}\,\}+\overset{\to }{\mathop{q}}\,\times \{(\overset{\to }{\mathop{x}}\,-\overset{\to }{\mathop{r}}\,))\times \overset{\to }{\mathop{q}}\,\}\]\[+\overset{\to }{\mathop{r}}\,\times \{(\overset{\to }{\mathop{x}}\,-\overset{\to }{\mathop{p}}\,)\times \overset{\to }{\mathop{r}}\,\}=\overset{\to }{\mathop{0}}\,\] then \[\overset{\to }{\mathop{x}}\,\] is given by
A.	\[\frac{1}{2}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,-2\overset{\to }{\mathop{r}}\,)\]
B.	\[\frac{1}{2}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,+\overset{\to }{\mathop{r}}\,)\]
C.	\[\frac{1}{3}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,+\overset{\to }{\mathop{r}}\,)\]
D.	\[\frac{1}{3}(2\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,-\overset{\to }{\mathop{r}}\,)\]
Answer» C. \[\frac{1}{3}(\overset{\to }{\mathop{p}}\,+\overset{\to }{\mathop{q}}\,+\overset{\to }{\mathop{r}}\,)\]

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