Question

A = 3i+4j and B = i+j+2k then find out unit vector along A+B

Answer 1

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Answer 2

As per the given data in the above question.

We have to find the unit vector of A+B

Given,

$A = 3 \hat i+4 \hat j$

$B = \hat i+\hat j+2 \hat k$

Solution:

$A+B=(3 \hat i+ 4 \hat j) + (\hat i+\hat j+2 \hat k)$

$A+B= (3 \hat i+ \hat i+4 \hat j + \hat j+2 \hat k)$

$A+B= (4 \hat i+5\hat j +2 \hat k)$

Unit vector : A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector.

$\hat a= \frac{a}{ |a| }$

Where |a| is for norm or magnitude of vector a.

Similarly,

$\hat(A+B) = \frac{A+B}{ |A+B| } \: \: \: \: \: ......(1)$

• First magnitude of A+B

$|A+B| = √ 4²+5²+2²$

$|A+B| = \sqrt{16 + 25 + 4}$

$|A+B| = \sqrt{45} \: \: \: \: \: \: \: ....(2)$

From (1) and (2) ,we get

$\hat(A+B)= \frac{(4 \hat i+5\hat j +2 \hat k)}{45}$

The unit vector is

$\hat(A+B)= \frac{4 \hat i}{45} + \frac{5\hat j }{5} + \frac{2 \hat k}{45}$

Project code #SPJ2