# What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # (4 i + 4 j + 2 k) #?

There are two steps in solving this question: (1) taking the cross product of the vectors and then (2) normalizing the resultant. In this case, the final unit vector is

The cross product of the vectors is the first step.

Normalizing the resulting vector is the second step.

Each element of a vector is normalized by dividing it by its length, which can be found as follows:

When everything is considered, the unit vector orthogonal to the supplied vectors can be expressed as follows:

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The unit vector orthogonal to the plane containing (i - 2j + 3k) and (4i + 4j + 2k) is (-6i + 10j - 8k) / sqrt(180).

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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.

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.

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 orthogonal to the plane containing # (-2i- 3j + 2k) # and # (3i – 4j + 4k) #?
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- What is the cross product of #<-3,0,1># and #<1,2,-4>#?
- Will a vector at 45° be larger or smaller than its horizontal and vertical components?

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