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For the vectors Bold uequalsleft angle negative 9 comma 0 comma 1 right angle and Bold vequalsleft angle 1 comma 5 comma negative 5 right angle​, calculate proj Subscript Bold v Baseline Bold u and scal Subscript Bold v Baseline Bold u.
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Part 1
proj Subscript Bold v Baseline Bold uequalsleft angle nothing comma nothing comma nothing right angle



Part 2
scal Subscript Bold v Baseline Bold uequals

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​(Type an exact​ answer, using radicals as​ needed.)



Answer :

lexie2fine

Answer:

To find the projection of u onto v, we need to calculate:

proj subscript v baseline u = ((u · v) / ||v||²) v

First, let's find the dot product u · v:

u · v = <-9, 0, 1> · <1, 5, -5> = -9(1) + 0(5) + 1(-5) = -14

Next, let's find the magnitude of v:

||v|| = √(1² + 5² + (-5)²) = √(1 + 25 + 25) = √51

Now, we can calculate the projection:

proj subscript v baseline u = ((-14) / (√51)²) v = (-14 / 51) v = (-14 / 51) <1, 5, -5> = <-14/51, -70/51, 70/51>

So, the projection of u onto v is:

proj subscript v baseline u = <-14/51, -70/51, 70/51>  

scal subscript v baseline u = (u · v) / ||v||

We already calculated the dot product u · v = -14 and the magnitude of v = √51.

So, we can plug in these values:

scal subscript v baseline u = (-14) / √51

To simplify, we can rationalize the denominator:

scal subscript v baseline u = (-14) / √51 × √51 / √51 = -14√51 / 51

So, the scalar component of u in the direction of v is:

scal subscript v baseline u = -14√51 / 51

Step-by-step explanation: