Question

If A = 3 i – 2j + 4 k and B = 3i + 4j -8k , then the value of A – B is​

Answer 1

Answer:

$\boxed{\mathfrak{\overrightarrow{A} - \overrightarrow{B} = 6(2\hat{k} - \hat{j})}}$

Given:

$\rm \overrightarrow{A} = 3\hat{i} - 2 \hat{j} + 4\hat{k} \\ \rm \overrightarrow{B} =3 \hat{i} + 4 \hat{j} - 8 \hat{k}$

Explanation:

$\rm \overrightarrow{A} - \overrightarrow{B} = 3\hat{i} - 2 \hat{j} + 4\hat{k} - (3 \hat{i} + 4 \hat{j} - 8 \hat{k}) \\ \\ \rm = 3\hat{i} - 2 \hat{j} + 4\hat{k} - 3 \hat{i} - 4 \hat{j} + 8 \hat{k}\\ \\ \rm = (3\hat{i} - 3\hat{i}) - (2 \hat{j} + 4 \hat{j} ) + (4\hat{k} + 8\hat{k} ) \\ \\ \rm = - 6 \hat{j} + 12\hat{k} \\ \\ \rm = 12\hat{k} - 6 \hat{j}\\ \\ \rm = 6(2\hat{k} - \hat{j})$

Answer 2

Answer:-

$\large\leadsto\boxed{\sf\purple{\overrightarrow{A} - \overrightarrow{B} = 6(2\hat{k} - \hat{j})}}$

• Given:-

$\sf \overrightarrow{A} = 3\hat{i} - 2 \hat{j} + 4\hat{k} \\ \sf \overrightarrow{B} =3 \hat{i} + 4 \hat{j} - 8 \hat{k}$

• To Find:-

$\sf{\overrightarrow{A} - \overrightarrow{B} =}$ = ?

• Solution:-

Subtraction of 2 Vectors:-

$\sf \overrightarrow{A} - \overrightarrow{B} = 3\hat{i} - 2 \hat{j} + 4\hat{k} - [3 \hat{i} + 4 \hat{j} - 8 \hat{k}] \\ \\ \sf = 3\hat{i} - 2 \hat{j} + 4\hat{k} - 3 \hat{i} - 4 \hat{j} + 8 \hat{k}\\ \\ \sf = - 6 \hat{j} + 12\hat{k} \\ \\ \sf = 12\hat{k} - 6 \hat{j}\\ \\ \sf = 6(2\hat{k} - \hat{j})$

$\pink{\bigstar}$ $\boxed{\sf\red{\overrightarrow{A} - \overrightarrow{B} = 6(2\hat{k} - \hat{j})}}$

$\orange{\bigstar}$ Some Additional information:-

• Vector Quantities are those which have both magnitude and direction and obey the triangle law of vector addition.

• Example:- Position, displacement, acceleration, force, weight...etc.

• To express a vector quantity completely direction must be also specified along with the magnitude.

• A vector can be represented by an arrow. This arrow is called 'vector'.The length of the arrow represents the magnitude and the tip of arrow [arrow-head] represents the direction.