Question

If vector a is 4i -3j and b vector is 6i +8j then magnitude and direction of vector a+b is

Answer 1

Given that...

a=4i-3j
b=6i+8j
so

a+b=(4i-3j)+(6i+8j)

a+b=10i+5j

so magnitude of a+b
=√(10^2+5^2)
=√(100+25)
=√(125)
=5√5

The vector a+b=10i+5j
by the diagram..
tan @=1/2
or
@=tan^-1(1/2)
so vector will make angle tan^-1(1/2) with positive x-axis

Answer 2

Explanation:

It is given that,

Vector 1, a = 4i - 3j

Vector 2, b = 6i + 8j

$a+b=(4i-3j)+(6i+8j)$

$a+b=10i-5j$

$|a+b|=\sqrt{10^2+(-5)^2}$

The magnitude of the vector, $|a+b|=11.1$

The direction of the vector is,

$\theta=tan^{-1}\dfrac{y}{x}$

$\theta=tan^{-1}\dfrac{-5}{10}$

$\theta=-26.5$

Hence, this is the required solution.