Correct Answer - Option 3 :
\(\frac{60}{\sqrt {114}}\)
CONCEPT:
- Projection of a vector \(\vec a\)on other vector \(\vec b\)is given by: \(\vec a \cdot \hat b = \frac{\vec a \cdot \vec b}{|\vec b|}\)
CALCULATION:
Let \(\vec a = \hat i + 3\hat j + 7\hat k \ and \ \vec b = 7\vec i - \vec j + 8\hat k\)
Here, we have to find the projection of a vector \(\vec a\) on other vector \(\vec b\) is given by: \(\vec a \cdot \hat b = \frac{\vec a \cdot \vec b}{|\vec b|}\)
⇒ \(\vec a \cdot \vec b = 7 - 3 + 56 = 60 \ and \ |\vec b| = \sqrt {114}\)
⇒ \(\vec a \cdot \hat b = \frac{60}{\sqrt {114}}\)
Hence, option 3 is correct.
