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shtirl [24]
2 years ago
7

Given that p=9i+12j and q=-6i-8j. Evaluate |p-q|-{|p|-|q|}

Mathematics
1 answer:
krok68 [10]2 years ago
7 0

Answer:

|p-q|-(|p|-|q|) = 20

Step-by-step explanation:

First let's find the value of 'p-q':

p - q = 9i + 12j - (-6i - 8j)\\p - q = 9i + 12j + 6i + 8j\\p - q = 15i + 20j\\

To find |p-q| (module of 'p-q'), we can use the formula:

|ai + bj| = \sqrt{a^{2}+b^{2}}

Where 'a' is the coefficient of 'i' and 'b' is the coefficient of 'j'

So we have:

|p - q| = |15i + 20j| = \sqrt{15^{2}+20^{2}} = 25

Now, we need to find the module of p and the module of q:|p| = |9i + 12j| = \sqrt{9^{2}+12^{2}} = 15

|q| = |-6i - 8j| = \sqrt{(-6)^{2}+(-8)^{2}} = 10

Then, evaluating |p-q|-{|p|-|q|}, we have:

|p-q|-(|p|-|q|) = 25 - (15 - 10) = 25 - 5 = 20

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