Match each displacement vector combination on the left with its corresponding resultant di… — JAMB UTME

Match each displacement vector combination on the left with its corresponding resultant displacement magnitude or vector on the right.

A walk of $3\text{ m}$ East followed by $4\text{ m}$ NorthA resultant magnitude of $5\text{ m}$
A walk of $5\text{ m}$ East followed by $12\text{ m}$ SouthA resultant magnitude of $13\text{ m}$
A walk of $8\text{ m}$ East followed by $6\text{ m}$ WestA resultant displacement of $2\text{ m}$ East
A walk of $9\text{ m}$ North followed by $12\text{ m}$ EastA resultant magnitude of $15\text{ m}$

The correct pairs correspond as follows:

3\text{ m}

East and

4\text{ m}

North matches a resultant magnitude of

5\text{ m}

;

5\text{ m}

East and

12\text{ m}

South matches a resultant magnitude of

13\text{ m}

;

8\text{ m}

East and

6\text{ m}

West matches a resultant displacement of

2\text{ m}

East; and

9\text{ m}

North and

12\text{ m}

East matches a resultant magnitude of

15\text{ m}

Each vector combination is resolved according to its directional alignment: perpendicular displacements require the Pythagorean theorem (

R = \sqrt{A^2 + B^2}

), whereas anti-parallel collinear displacements require vector subtraction.

Identify orthogonal vector scenarios

Perpendicular displacement vectors form right-angled triangles.

Directions such as East-North, East-South, and North-East are at

90^\circ

relative to one another.

Calculate magnitudes for orthogonal pairs using the Pythagorean theorem

For

3\text{ m}

and

4\text{ m}

\sqrt{3^2 + 4^2} = 5\text{ m}

. For

5\text{ m}

and

12\text{ m}

\sqrt{5^2 + 12^2} = 13\text{ m}

. For

9\text{ m}

and

12\text{ m}

\sqrt{9^2 + 12^2} = 15\text{ m}

The magnitude of two perpendicular vectors

\vec{A}

and

\vec{B}

is given by

R = \sqrt{A^2 + B^2}

Calculate net displacement for opposite collinear vectors

For

8\text{ m}

East and

6\text{ m}

West:

8 - 6 = 2\text{ m}

East.

Vectors pointing in opposite directions along the same axis subtract algebraically, retaining the direction of the vector with the greater magnitude.

Addition of Perpendicular and Collinear Displacement Vectors

Estimated Time:1m 30s

Question