Question
Asked Sep 22, 2019
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Find two unit vectors orthogonal to a=⟨−3,−4,−4⟩ and b=⟨−5,0,5⟩
Note: Enter your answers so that the first vector has a positive first coordinate.

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Expert Answer

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Step 1

Given that

a=(-3,-4,-4) and b=(-5,0,5)
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a=(-3,-4,-4) and b=(-5,0,5)

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Step 2

To find the unit vectors first find the value of a × b as it is orthogonal to both a and b.

k
i
j
axb3 -4
0
-3
5
0
(-4)(3)-(0.0--3)( -3) -5-0]+k[(-3)-0-5-(-4)]
i(12)-(9) k(20)
(12,-9,20)
+
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k i j axb3 -4 0 -3 5 0 (-4)(3)-(0.0--3)( -3) -5-0]+k[(-3)-0-5-(-4)] i(12)-(9) k(20) (12,-9,20) +

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Step 3
Find the value of laxb|| as follows.
ax b=(12) +(-9)+ (20)
= 625
- 25
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Find the value of laxb|| as follows. ax b=(12) +(-9)+ (20) = 625 - 25

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