Question

if x and y components of a vector vector P have numerical values 3 and 4 respectively and that affected p p + vector Q have numerical values 8 and 7 respectively then the magnitude of vector Q is​

Answer 1

If vector P + vector Q have numerical values 8 and 7 respectively then the magnitude of vector Q is  5.83.

Explanation:

The x and y components of vector P is given as 3 and 4 respectively i.e.,  

Vector P = 3i + 4j …… (i)

The x and y component of vector P + vector Q is given as 8 and 7 respectively i.e.,  

Vector (P + Q) = 8i + 7j ……. (ii)  

Let’s assume the vector Q = “xi + yj” ….. (iii)

Now, adding (i) & (iii) and equating with (ii), we get

[3i + 4j] + [xi + yj] = [8i + 7j]  ……. (iv)

From eq. (iv), we can write two equations to get the value of vector Q,

3 + x = 8

⇒ x = 8 – 3

⇒ x = 5  

And,  

4 + y = 7

⇒ y = 7 – 4

⇒ y = 3

∴ Vector Q = 5i + 3j

Thus,  

The magnitude of vector Q is given as,

= $\sqrt{5^2 + 3^2}$

=  $\sqrt{25 + 9}$  

= $\sqrt{34}$  

= 5.83

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Answer 2

The magnitude of vector Q=$\sqrt{34}$

Explanation:

x and y component of vector P are 3 and 4.

Therefore, $\vec{P}=3\hat{i}+4\hat{j}$

$\vec{P}+\vec{Q}=8\hat{i}+7\hat{j}$

We have to find the value of magnitude of vector Q.

Substitute the value of P

Then, we get

$3i+4j+\vec{Q}=8i+7j$

$\vec{Q}=8i+7j-3i-4j=5i+3j$

$\mid Q\mid=\sqrt{(5)^2+(3)^2}=\sqrt{34}$

Hence, the magnitude of Q =$\sqrt{34}$

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