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Chapter 9: Q. 45 (page 630)

In Problems 40鈥�45, use the vectors v=3i+j-2kand w=-3i+2j-kto find each expression.

Find a unit vector orthogonal to both v and w.

Short Answer

Expert verified

The unit vector 3i+9j+9kis orthogonal to bothvandw.

Step by step solution

01

Step 1. Given Information 

The given vectors arev=3i+j-2kandw=-3i+2j-k.

02

Step 2. Finding the unit vector

By using the geometric property of the cross product, if uand vare vectors in space then u脳v is orthogonal to both uand v.

So, to find the unit vector which is orthogonal to bothvandwlet's find the cross product.

03

Step 3. Solve

By using the formula of the cross product v脳w=b1c2-b2c1i-a1c2-a2c1j+a1b2-a2b1k

So, the unit vector is

v脳w=1路-1-2路-2i-3路-1--3路-2j+3路2--3路1kv脳w=3i+9j+9k

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