Question

find the unit vector of vector A +vector B where vector A=2i^-j^+3k^ and vector B=3i^-2j^-2k^​

Answer 1

Answer:

(1/√35) (5i - 3k + k)

Explanation:

vec.A + vec.B = 2i - j + 3k + 3i - 2j - 2k

                       = 5i - 3j + k

Resultant of vec.A and vec.B = 5i - 3j + k.

Magnitude of resultant is √5² + 3² + 1²

                         = √25 + 9 + 1

                         =  √35

Unit vector = vector/magnitude

                  = (5i - 3i + k)/√35

Answer 2

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

$\sf{ \vec{B} = 3\hat{i} - 2 \hat{j} -2 \hat{k} }$

$\sf{ \vec{A} + \vec{B} = 2 \hat{i} - \hat{j} +3 \hat{k} + 3\hat{i} - 2 \hat{j} -2 \hat{k}}$

» $\sf{ \vec{A} + \vec{B} = 5 \hat{i} - 3 \hat{j} + \hat{k} }$

$\sf{ | \vec{A} + \vec{B} | = |5 \hat{i} -3 \hat{j} + \hat{k} |}$ = $\sf {\sqrt{5^{2} + 3^{2} + 1^{1}} }$ = √35

Thus, unit vector = $\sf { \frac{ 5 \hat{i} - 3 \hat{j} + \hat{k} }{\sqrt{35}} }$