Question

Find the projection of vector \((\hat i-\hat j)\) on vector \((\hat i+\hat j)\).

Hint:

Projection formula \(=\dfrac{\vec a\cdot\vec b}{|\vec b|}\); here the dot product is zero.

Answer 1

Step 1: Understanding the Concept:
The projection of vector \(\vec a\) on vector \(\vec b\) is \(\dfrac{\vec a\cdot\vec b}{|\vec b|}\).

Step 2: Computing the dot product:
\(\vec a=\hat i-\hat j\), \(\vec b=\hat i+\hat j\). \(\vec a\cdot\vec b=(1)(1)+(-1)(1)=1-1=0\).

Step 3: Computing the projection:
Since the numerator is 0, the projection is \(\dfrac{0}{|\vec b|}=0\), regardless of \(|\vec b|\).

Final Answer:
Projection \(=\boxed{0}\).