Question

write the value of 5 i cap + 3 J cap 5 i cap - 3 J cap​

Answer 1

Question

Find the value of sum of given vectors

$\tt{ \vec{a} = 5 \hat{i} + 3 \hat{j}} \\ \\ \tt{and \: \vec{b} = 5 \hat{i} - 3 \hat{j}}$

Solution

Given,

$\tt{ \vec{a} = 5 \hat{i} + 3 \hat{j}} \\ \\ \tt{and \: \vec{b} = 5 \hat{i} - 3 \hat{j}}$

To finD

Sum of the Vectors

Now,

$\tt{ \vec{a} + \vec{b}} \\ \\ = \tt{(5 \hat{i} + 3 \hat{j}) + (5 \hat{i} - 3 \hat{j})} \\ \\ = \huge{ \tt{10 \hat{i}}}$

Magnitude of the vector sum :

$\large{| \tt{\vec{a} + \vec{b}}| = | \tt{10 \hat{i}}| = \sqrt{{10}^{2}} \: \: = \tt{10 \ units}}$

• Magnitude of a Unit Vector is one