Question

Plane $OXY$ satisfying $OA\cdot \hat{i}=1$ and $OB\cdot \hat{i}=-2$, then the length of the vector $2OA-3OB$ assuming that the second component of each vector is equal to the square of the first component

• A. $\sqrt{14}$
• B. $2\sqrt{51}$
• C. $3\sqrt{41}$
• D. none of these

Answer 1

Answer: (D)

none of these

Let $OA=x_{1}i+y_{1}j$ and $OB=x_{2}i+y_{2}j$.
Since $1=OA.i=x_1$ and $-2=OB.i=x_2.$
Moreover, $y_1=x_1^2=1$ and $y_2=x_2^2=4,$
so $OA=i+j$ and $OB=-2i+4j.$
Hence $|2OA-3OB|=|8i-10j|=\sqrt{164}=2\sqrt{41}.$