Question

For v1 =2i-3j and v2=-6i+5j determine the magnitude and direction of v1+v2

Answer 1

answer : magnitude = 2√5 and direction : 26.57° with x-axis.

two vectors are v1 = 2i - 3j and v2 = -6i + 5j

then, v1 + v2 = (2i - 3j) + (-6i + 5j)

= (-4i + 2j)

so, v1 + v2 = (-4i + 2j)

magnitude of vector , |v1+v2| = √{(-4)² + (2)²} = 2√5 unit

now we have to find direction of (v1 + v2).

we know, if V = a i + b j is a standard vector then it makes an angle tan^-1|(b/a)| with x-axis.

similarly, vector , (v1 + v2) makes an angle tan^-1|(2/-4)| = tan^-1(1/2) ≈ 26.57° with x-axis.

Answer 2

Answer:

magnitude = 2√5 and direction : 26.57° with x-axis.

Explanation:

two vectors are v1 = 2i - 3j and v2 = -6i + 5j

then, v1 + v2 = (2i - 3j) + (-6i + 5j)

= (-4i + 2j)

so, v1 + v2 = (-4i + 2j)

magnitude of vector , |v1+v2| = √{(-4)² + (2)²} = 2√5 unit

now we have to find direction of (v1 + v2).

we know, if V = a i + b j is a standard vector then it makes an angle tan^-1|(b/a)| with x-axis.

similarly, vector , (v1 + v2) makes an angle tan^-1|(2/-4)| = tan^-1(1/2) ≈ 26.57° with x-axis.