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2 months ago

If a =5, 0, −1,find a vector b such that compab = 2.b = _______.

Mathematics

1 answer:

PIT_PIT [12.4K]2 months ago

7 0

Response:

$b = (q,r , 5q-2\sqrt{26} )$

Step-by-step breakdown:

According to the question,

The provided vector is

$a = (5,0,-1)$

Additionally $comp_a b = 2$

Generally

$comp_a b = \frac{a \cdot b}{|a|}$

Here $|a|$ represents the magnitude of a, expressed mathematically as

$|a| = \sqrt{5^2 + 0^2 +(-1)^2 }$

=> $|a| = \sqrt{26}$

b is a vector that we can assume has the following characteristics

$b = (q , r , x)$

Thus

$comp_a b = \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } = 2$

=> $\frac{5q + 0 -x}{\sqrt{26} } = 2$

=> $x = 5q-2\sqrt{26}$

Consequently, the vector can be mathematically expressed as

$b = (q,r , 5q-2\sqrt{26} )$

This implies that vector b includes multiple values as it consists of variables.

This indicates that if

$q = 1\\r=1\\x =1$

Then

$b = (1,1,5-2\sqrt{26} )$

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