What vector must be added to the two vectors i- 2j + 2k and 2i+j-k tha

1.	What vector must be added to the two vectors i- 2j + 2k and 2i+j-k that the resultant may be a unit vector along x axis
Answer» ANSWER: The vector that must be added is $-2\hat i+\hat j-\hat k$ Explanation: UNIT vector ALONG x-axis is $\hat i$ Let the vector added is $a_1\hat i+a_2\hat j+a_3\hat k$ Therefore $(\hat i-2\hat j+2\hat k)+(2\hat i+\hat j-\hat k)+(a_1\hat i+a_2\hat j+a_3\hat k)=\hat i$ $\implies 3\hat i-\hat j+\hat k+a_1\hat i+a_2\hat j+a_3\hat k=\hat i$ $\implies (3+a_1)\hat i+(a_2-1)\hat j+(a_3+1)\hat k=\hat i$ Comparing both the sides $a_1+3=1\implies a_1=-2$ $a_2-1=0\implies a_2=1$ $a_3+1=0\implies a_3=-1$ Therefore, the vector that must be added is $-2\hat i+\hat j-\hat k$ Hope this answer is helpful.