Question

the resultant of two vectors is perpendicular to one of them and has the magnitude 4m if the sum of the magnitude of two vectors is 8m then ​

Answer 1

Answer:

this is the answer

Explanation:

given

$\alpha = 90$

Answer 2

Answer:

Magnitude of two vector = 3 & 5

Explanation:

the resultant of two vectors is perpendicular to one of them and has the magnitude 4m if the sum of the magnitude of two vectors is 8m then ​

Let say two vectors are A & B

and resultant Vector = C

To simplify Let say

A =  Xi   => Magnitude of Vector A = X

Then resultant Vector C =  4j  m

Perpendicular to one of vector with magnitude 4m

Vector B = Vector C  - Vector A

=> B =  4j - Xi

Magnitude of B = √(4² + X²)

sum of the magnitude of two vectors is 8m

=> X + √(4² + X²) = 8

=> √(16 + X²)  = 8 - X

Squaring both sides

16 + X² = 64 + X² - 16X

=> 16X = 48

=> X = 3

Vector A = 3i   => Magnitude = 3

Vector B = -3i + 4j  => Magnitude = √(-3)² + 4² = 5

Vector C = 4j

Magnitude of two vector = 3 & 5