Question

If \[ \vec a=\hat i-\hat j+2\hat k,\qquad \vec b=-\hat i+2\hat j \] and \(\vec c\) are three vectors such that \(\vec a+\vec b\) is parallel to \(\vec c\) and \[ (\vec c+\vec a)\cdot(\vec c+\vec b)=7, \] then the vector \(\vec c\) having minimum length is

• A. \(\dfrac{1}{2}\hat j+\hat k\)
• B. \(\hat j+2\hat k\)
• C. \(-2\hat j-4\hat k\)
• D. \(\dfrac{1}{3}\hat j+\dfrac{2}{3}\hat k\)

Hint:

Whenever one vector is parallel to another, write it as a scalar multiple. Substitute into the given vector equation, solve for the scalar, and then compare magnitudes if a minimum or maximum length is required.

Answer 1

The Correct Option is B