Question

Determine the magnitude of the sum of the three vectors: V1=6.0i^−7.0j^,V2=i^+j^, and V3=−1.0i^+4.0j^

Answer 1

6.32 units

Step-by-step explanation:

`V_1=6.0 \hat {i} -7.0\hat{j}\\ V_2=\hat {i} +\hat{j}\\ V_3=-1.0 \hat {i} +4.0\hat{j}`

Adding the vectors

`V_1+V_2+V_3=(6+1-1)\hat {i}+(-7+1+4)\hat {j}\\\Rightarrow V=6\hat {i}-2\hat {j}`

`|V|=√(6^2+(-2)^2)\\\Rightarrow |V|=√(36+4)\\\Rightarrow |V|=√(40)\\\Rightarrow |V|=6.32\ units`

∴ Magnitude of the sum of the three vectors is 6.32 units