Question

the length of the vector a=3i metre and b=4j metre

Answer 1

Explanation:

Step 1: Calculate magnitude of vector B

Magnitude of vector B = sqrt(7^2 + 24^2) = sqrt(625) =25

Step 2: Calculate unit vector of Vector A

Unit Vector A = Vector A/ Magnitude of A

Magnitude of A = sqrt(3^2 + 4^2) = sqrt(25) = 5

Hence Unit Vector A = (3i+4j)/5 = (3/5)i + (4/5)j

Step 3: Calculating Vector magnitude of B and parallel to A

Required Vector Say C = Magnitude of B * Unit vector of A

Hence C = 25*((3/5)i+(4/5)j) =25*(3/5)i + 25*(4/5)j

C = 15 i + 20 j

Step 4 : Verify

Magnitude of Vector C = sqrt(15^2 + 20^2) =sqrt(625) = 25 = Magnitude of Vector B

Check angle of vector A and Vector C

Angle of Vector A = taninverse(4/3) = 53.1301 degrees

Angle of Vector C = taninverse(20/15) = taninverse(4/3) = 53.1301 degrees

Result :

Hence Vector C = 15i + 20j has direction of Vector A and magnitude of Vector B