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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise 22.9 Question 8 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise 22.9 Question 8 Maths Textbook Solution.

Answers (1)

Answer: Direction cosines are equal

Given: Show that the vector \hat{i}+\hat{j}+\hat{k}is equally inclined with the axis OX, OY and OZ.

Hint: Find \mid \vec{a}\midthen direction direction cosines

Explanation: Let \vec{a}=\hat{i}+\hat{j}+\hat{k}=1 \hat{i}+1 \hat{j}+1 \hat{k}

A vector is equally inclined to OX, OY, OZ

i.e. X, Y and Z axis respectively.

If its direction cosines are equal

Direction ratios of \vec{a} are a=1,b=1,c=1

Magnitude of \begin{aligned} &\vec{a}=\sqrt{1^{2}+(1)^{2}+(1)^{2}} \\ \end{aligned}

\begin{aligned} &|\vec{a}|=\sqrt{3} \\ \end{aligned}

Direction cosines of  \begin{aligned} &|\vec{a}| \text { are }\left(\frac{a}{|\vec{a}|}\left|\frac{b}{\mid \vec{b}}\right|^{\prime} \mid \overrightarrow{\vec{c} \mid}\right) \\ \end{aligned}

\begin{aligned} &=\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right) \end{aligned}

Since the direction cosines are equal

\vec{a}=\hat{i}+\hat{j}+\hat{k}is equally inclined to OX, OY and OZ.

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