Question

find a unit vector in direction of the resultant of vectors A=2i-3j+k, B, = i +j+2k and C =3i-2j+4k

Answer 1

Answer:

Explanation:

Complete answer is given on the image uploaded, you can go through that.

Thankyou.

Answer 2

Answer:

The unit vector in the direction of the resultant is $\frac{6\hat{i}-4\hat{j}+7\hat{k}}{\sqrt{101} }$.

Explanation:

            The resultant of vectors=sum of vectors              (1)

The vectors given in the question are,

$\vec{A}=2\hat{i}-3\hat{j}+\hat{k}$       (2)

$\vec{B}=\hat{i}+\hat{j}+2\hat{k}$         (3)

$\vec{C}=3\hat{i}-2\hat{j}+4\hat{k}$     (4)

So, the resultant of all the three vectors are as follows,

$\vec{R}=\vec{A}+\vec{B}+\vec{C}$         (5)

By placing equations (2),(3), and (4) in equation (5) we get;

$\vec{R}=2\hat{i}-3\hat{j}+\hat{k}+\hat{i}+\hat{j}+2\hat{k}+3\hat{i}-2\hat{j}+4\hat{k}$

$\vec{R}=2\hat{i}+\hat{i}+3\hat{i}-3\hat{j}+\hat{j}-2{j}+\hat{k}+2\hat{k}+4\hat{k}$

$\vec{R}=6\hat{i}-4\hat{j}+7\hat{k}$     (6)

And the magnitude of equation (6) is calculated as,

$|\vec{R}|=\sqrt{6^2+4^2+7^2}$

$|\vec{R}|=\sqrt{36+16+49}$

$|\vec{R}|=\sqrt{101}$        (7)

The unit vector(U) in the direction of resultant is calculated as,

$U=\frac{\vec{R}}{|\vec{R}|}$          (8)

By placing equations (6) and (7) in equation (8) we get;

$U=\frac{6\hat{i}-4\hat{j}+7\hat{k}}{\sqrt{101} }$

Hence, the unit vector in the direction of the resultant is $\frac{6\hat{i}-4\hat{j}+7\hat{k}}{\sqrt{101} }$.

#SPJ2