Question

If \(\vec a\) is a vector perpendicular to the plane containing the vectors \[ 2\hat i-\hat j+3\hat k \quad\text{and}\quad -\hat i+3\hat j+2\hat k, \] then the magnitude of the projection of the vector \[ 3\hat i+2\hat j-\hat k \] on \(\vec a\) is

• A. \(\dfrac{24}{\sqrt{195}}\)
• B. \(\dfrac{42}{\sqrt{195}}\)
• C. \(2\sqrt{\dfrac{13}{15}}\)
• D. \(4\sqrt{\dfrac{13}{15}}\)

Hint:

If a vector is perpendicular to the plane containing two vectors \(\vec u\) and \(\vec v\), then \[ \boxed{\vec a\parallel(\vec u\times\vec v)}. \] After finding the normal vector, use \[ \boxed{\text{Projection}=\frac{|\vec x\cdot\vec a|}{|\vec a|}}. \]

Answer 1

The Correct Option is D