Find \( v \cdot u \) \( v=-4 i+6 j \) and \( u=9 i+9 j \) 18 \( 5 i+15 j \) \( -36 i+54 j \) \( -90 \)
brandon9126
To find the dot product of \( v \) and \( u \), you multiply the corresponding components of the vectors and then sum them.
Given:
\( v = -4i + 6j \)
\( u = 9i + 9j \)
The dot product, \( v \cdot u \), is given by:
\( v \cdot u = (-4)(9) + (6)(9) \)
Evaluating the expression:
\( v \cdot u = -36 + 54 \)
\( v \cdot u = 18 \)
Therefore, the dot product of \( v \) and \( u \) is 18.
To find the dot product \( v \cdot u \), we need to multiply the corresponding components of the two vectors and sum them up.
Given:
\( v = -4i + 6j \)
\( u = 9i + 9j \)
Step 1: Multiply the corresponding components.
\( v \cdot u = (-4)(9i) + (-4)(9j) + (6)(9i) + (6)(9j) \)
Step 2: Simplify.
\( v \cdot u = -36i + (-36j) + 54i + 54j \)
Step 3: Combine like terms.
\( v \cdot u = (-36i + 54i) + (-36j + 54j) \)
Step 4: Simplify further.
\( v \cdot u = 18i + 18j \)
Therefore, the dot product \( v \cdot u \) is \( 18i + 18j \).