What is the unit vector that is normal to the plane containing <2i+7j-2k> and <8i-2j+3k>?

Answer 1

Olivia Askew

The unit vector is #=1/sqrt(4373)*〈17,-22,-60〉#

Using the determinant (cross product), one can calculate the vector perpendicular to two vectors.

#| (veci,vecj,veck), (d,e,f), (g,h,i) | #

where #〈d,e,f〉# and #〈g,h,i〉# are the 2 vectors

Here, we have #veca=〈2,7,-2〉# and #vecb=〈8,-2,3〉#

Consequently,

#| (veci,vecj,veck), (2,7,-2), (8,-2,3) | #

#=veci| (7,-2), (-2,3) | -vecj| (2,-2), (8,3) | +veck| (2,7), (8,-2) | #

#=veci(7*3-2*2)-vecj(2*3+8*2)+veck(2*-2-7*8)#

#=〈17,-22,-60〉=vecc#

Verification using the two dot method

#〈17,-22,-60〉.〈2,7,-2〉=17*2-22*7-60*-2=0#

#〈17,-22,-60〉.〈8,-2,3〉=17*8-22*-2-60*3=0#

Thus,

#vecc# is perpendicular to #veca# and #vecb#

The vector of units is

#hatc=vecc/||c||=1/sqrt(4373)*〈17,-22,-60〉#

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Answer 2

Benjamin Asiedu

The unit vector normal to the plane containing <2i+7j-2k> and <8i-2j+3k> is <13/√182, 44/√182, 20/√182>.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

What is the unit vector that is normal to the plane containing &lt;2i+7j-2k&gt; and &lt;8i-2j+3k&gt;?

What is the unit vector that is normal to the plane containing <2i+7j-2k> and <8i-2j+3k>?