Find a unit vector orthogonal to both u and v.

Question

u = i + 2j

v = i + 3k

Answer 1

Given:

u = i + 2j

v = i + 3k

To find a unit vector orthogonal to both u and v, the formula is:

→ →

u × v

→ →

||u × v||

→ → | i j k |

u × v = | 1 2 0 |

| 1 0 3 |

= +i (6-0) - j(3-0) + k(0-2)

= 6i - 3j - 2k

→ →

||u × v|| = (6² + 3² + (-2)²)^1/2 = (36+9+4)^1/2

= (49)^1/2 = 7

Therefore:

→ →

u × v = (6/7)i - (3/7)j - (2/7)k

→ →

||u × v||