Question

the resultant of the two vectors A and B of magnitude 6 and 10 cm respectively is at right angle to the vector A find the resultant and also angle between the given vectors

Answer 1

Answer:

Magnitude of resultant vector = 8 cm

Angle = 53°

Explanation:

The resultant of the two vectors A and B of magnitude 6 cm and 10 cm respectively.

The resultant vector is at right angle with vector A.

Let resultant vector be C

The three vector form a right angle triangle.

where, vector B form Hypotenuse.

A and C vector form sides of triangle,

|B|=10 cm

|A|=6 cm

|C|=?

Using Pythagoras theorem,

$|B|^2=|A|^2+|C|^2$

$10^2=6^2+|C|^2$

$|C|=8\text{ cm}$

Let the angle between the vector A and B be Ф

$\cos\theta =\dfrac{|A|}{|B|}$

$\theta=\cos^{-1}\frac{6}{10}$

$\theta=53^\circ$

Hence, The magnitude of resultant vector is 8 cm and the angle between A and B is 53°

Answer 2

Explanation:

In this we can do it by using triangle law of addition or u can also apply parallelogram law of addition just make sure that the angle between the 2 vectors must be greater that 90° as resultant comes between the vector