Question

A.) Draw the vector C⃗ =A⃗ +2B⃗ .

B.)Draw the vector C⃗ =1.5A⃗ −3B⃗ .

C.)Draw the vector C⃗ =0.5A⃗ +2B⃗ .

Answer 1

Concepts and reason

The concepts used to draw the vectors are vectors and the vector diagram.

First use the concept of vectors to determine the relative magnitudes of the vectors in the combination and then draw the vectors by using the concept of vector diagrams.

Fundamentals

Vector is a physical quantity which is having both magnitude and direction.

The operation performed to add two or more vectors is known as vector addition.

The diagrams which represent the direction and the relative magnitude of the vector quantity by a vector arrow are known as vector diagrams.

(A)

The vector is given by,

Here, is the unit vector along x- direction.

The vector is given by,

The vector is a combination of vectors and , and is given by,

Substitute for and for in above equation as follows:

The following figure shows the vector diagram of the vectors.

The vector is having the magnitude of 4 and is directed along the positive x- axis, vector is having the magnitude of 1 and is directed along the negative x- axis.

(B)

The vector is given by,

Here, is the unit vector along x- direction and is the unit vector along y- direction.

The vector is given by,

The vector is a combination of vectors and and is given by,

Substitute for and for in above equation as follows:

(C)

The vector is given by,

Here, is the unit vector along x- direction and is the unit vector along y- direction.

The vector is given by,

The vector is a combination of vectors and and is given by,

Substitute for and for in above equation as follows:

Ans: Part A

Part B

Part C