# Y-component of Vector A if Vectors A and B are Orthogonal

**Problem**

Compute the value of *b* if **A** and **B** are orthogonal.

$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

A. 6 | C. 4 |

B. 5 | D. 3 |

**Answer Key**

[ D ]

**Solution**

Orthogonal means perpendicular. For perpendicular vectors, their dot product is zero.

${\bf A} \cdot {\bf B} = 0$

${\bf A} \cdot {\bf B} = 0$

$2(4) + b(-2) + 1(-2) = 0$

$2b = 6$

$b = 3$ ← Answer: [ D ]

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