Question

If two vectors A and B are orthogonal .then magnitude of their resultant is what?
a. (A+B)
b.(A squ +B squ)
c.root of (A+B)
d. root of (A squ +B squ)

Answer 1

Answer:

d. root of (A squ + Bsqu)

Answer 2

Given:

• A and B are orthogonal

To find:

• Magnitude of their resultant?

Calculation:

The general expression for resultant of two vectors is:

$\rm \: r = \sqrt{ {A}^{2} + {B}^{2} + 2. A.B. \cos( \theta) }$

• $\theta$ = 90° because the vectors are orthogonal (or perpendicular).

$\rm \implies \: r = \sqrt{ {A}^{2} + {B}^{2} + 2. A.B. \cos( {90}^{ \circ} ) }$

$\rm \implies \: r = \sqrt{ {A}^{2} + {B}^{2} + 2. A.B. (0) }$

$\rm \implies \: r = \sqrt{ {A}^{2} + {B}^{2} + 0 }$

$\boxed{ \rm \implies \: r = \sqrt{ {A}^{2} + {B}^{2}} }$

Or , we can also write as:

$\boxed{ \rm \implies \: r = root(A \: squ + B \: squ )}$

So, option d) is correct ✔️