Question

The sum of two vectors is 18 unit and smaller one has magnitude 5 units. If resultant is at 90° with smaller vector then magnitude of their resultant is
Answer: 12 units

Answer 1

Answer:

let r be resultant vector

given

r=√(x1^2+x2^2+2x1x2cos90°)

r=√(5^2+x2^2+0). { cos90°=0}

r=√(25+x2^2)

squaring on both sides

r^2=25+x2^2

Answer 2

Answer:

The magnitude of resultant is 12 units.

Explanation:

Given that,

Sum of two vectors R= 18 unit

Magnitude of smaller one B= 5 units

Angle = 90°

Suppose sum of vector is R, smaller one is A and larger one is B.

We need to calculate the magnitude of larger one

$A=18-5=13\ units$

We need to calculate the magnitude of resultant

Using Pythagorean theorem

$R=\sqrt{A^2-B^2}$

Put the value into the formula

$R=\sqrt{13^2-5^2}$

$R=12\ units$

Hence, The magnitude of resultant is 12 units.