Two vectors are given by A = 3 i ^ + 2 j ^ − k ^ and B = i ^ − 4 j ^ + 3 k ^ . Find the magnitude of the vector A + B .

First, find the resultant vector R = A + B . R = ( 3 + 1 ) i ^ + ( 2 − 4 ) j ^ + ( − 1 + 3 ) k ^ = 4 i ^ − 2 j ^ + 2 k ^ . Next, calculate its magnitude: ∣ R ∣ = 4 2 + ( − 2 ) 2 + 2 2 = 16 + 4 + 4 = 24 .

Start Free Mock LoginAlready registered? Login here

Physics - Vectors Question with Solution | TestHub

PhysicsVectorsAddition/SubtractionEasy2 minai-gemini

PhysicsEasysingle choice

Two vectors are given by $A = 3 \hat{i} + 2 \hat{j} - \hat{k}$ and $B = \hat{i} - 4 \hat{j} + 3 \hat{k}$ . Find the magnitude of the vector $A + B$ .

Options:

Answer:

Solution:

First, find the resultant vector $R = A + B$ . $R = (3 + 1) \hat{i} + (2 - 4) \hat{j} + (- 1 + 3) \hat{k} = 4 \hat{i} - 2 \hat{j} + 2 \hat{k}$ . Next, calculate its magnitude: $∣ R ∣ = 4^{2} + (- 2)^{2} + 2^{2} = 16 + 4 + 4 = 24$ .

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Addition/Subtraction

⏱ 2mℹ️ Source: ai-gemini

Doubts & Discussion

Loading discussions...