Chapter 3: Q27P (page 58)

If $\vec{d_{1}} + \vec{d_{2}} = 5 \vec{d_{3}}, \vec{d_{1}} - \vec{d_{2}} = 3 \vec{d_{3}}$ and $\vec{d_{3}} = 2 \hat{i} + 4 \hat{j}$ unit vector notation (a) $\vec{d_{1}}$ and (b) $\vec{d_{2}}$ ?

Short Answer

Expert verified

(a) $\vec{d_{1}} = 8 \hat{i} + 16 \hat{j}$

(b) $\vec{d_{3}} = 2 \hat{i} + 4 \hat{j}$

Step by step solution

Given data

The following information is given.

$\vec{d_{1}} + \vec{d_{2}} = 5 \vec{d_{3}}$ (i)

$\vec{d_{1}} - \vec{d_{2}} = 3 \vec{d_{3}}$ (ii)

$\vec{d_{3}} = 2 \hat{i} + 4 \hat{j}$ (iii)

Understanding the concept

Use the vector addition and vector subtraction laws to calculate the values of vector $\vec{d_{1}}$ and $\vec{d_{2}}$ .

Determination ofd1 andd2.

To calculate the values of vectors, add equations (i) and (ii) as follows:

$\begin{array}{rcl} (\vec{d_{1}} + \vec{d_{2}}) + (\vec{d_{1}} - \vec{d_{2}}) & = & 5 \vec{d_{3}} + 3 \vec{d_{3}} \\ = & 8 \vec{d_{3}} \\ 2 \vec{d_{1}} & = & 8 \vec{d_{3}} \\ \vec{d_{1}} & = & 4 \vec{d_{3}} \end{array}$

From equation (iii),

$\vec{d_{1}} + \vec{d_{2}} = 5 \vec{d_{3}}$

Substituting the value of $\vec{d_{1}}$ , we get

$\vec{d_{2}} = \vec{d_{3}}$

Therefore, the vector in $\vec{d_{2}}$ unit vector notation is,

$\vec{d_{2}} = 2 \hat{i} + 4 \hat{j}$

Now, use the value of $\vec{d_{2}}$ to calculate the $\vec{d_{1}}$

$\begin{array}{rcl} \vec{d_{1}} & = & 4 \times \vec{d_{3}} \\ = & 4 \times (2 \hat{i} + 4 \hat{j}) \\ = & 8 \hat{i} + 16 \hat{j} \end{array}$

Therefore, $\vec{d_{1}} = 8 \hat{i} + 16 \hat{j}$ androle="math" localid="1660886521162" $\vec{d_{2}} = 2 \hat{i} + 4 \hat{j}$

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If $\vec{d_{1}} + \vec{d_{2}} = 5 \vec{d_{3}}, \vec{d_{1}} - \vec{d_{2}} = 3 \vec{d_{3}}$ and $\vec{d_{3}} = 2 \hat{i} + 4 \hat{j}$ unit vector notation (a) $\vec{d_{1}}$ and (b) $\vec{d_{2}}$ ?

Short Answer

Step by step solution

Given data

Understanding the concept

Determination ofd1 andd2.

One App. One Place for Learning.

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If d1→+d2→=5d3→,d1→-d2→=3d3→andd3→=2i^+4j^unit vector notation (a) d1→and (b)d2→?

Short Answer

Step by step solution

Given data

Understanding the concept

Determination ofd1 andd2.

One App. One Place for Learning.

Most popular questions from this chapter

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If $\vec{d_{1}} + \vec{d_{2}} = 5 \vec{d_{3}}, \vec{d_{1}} - \vec{d_{2}} = 3 \vec{d_{3}}$ and $\vec{d_{3}} = 2 \hat{i} + 4 \hat{j}$ unit vector notation (a) $\vec{d_{1}}$ and (b) $\vec{d_{2}}$ ?