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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 19 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 19 Maths Textbook Solution.

Answers (1)

Answer: 6(\sqrt{2} \hat{i}+\hat{j}-\hat{k})

Hint: You must know the rules of vector functions

Given: Write a vector of magnitude 12 units which makes 45^{0} angles with x-axis, 60^{0}angle with y-axis, obtuse angle with z- axis.

Solution: Suppose a vector \vec{r}makes an angle 45^{0} with OX, 60^{0} with OY and having magnitude 12 units.

l=\cos 45^{\circ}=\frac{1}{\sqrt{2}} \text { and } m=\cos 60^{\circ}=\frac{1}{2}

Now,

\begin{aligned} &l^{2}+m^{2}+n^{2}=1 \\ &\frac{1}{2}+\frac{1}{4}+n^{2}=1 \\ &n^{2}=1-\frac{1}{2}-\frac{1}{4} \end{aligned}

\begin{aligned} &n^{2}=\frac{1}{4} \end{aligned}

\begin{aligned} &n^{2}=\pm \frac{1}{4} \end{aligned}

But angle obtuse angle along z-axis, so we use negative value.

∴  \begin{aligned} &n^{2}= \frac{-1}{4} \end{aligned}

Therefore,

\begin{aligned} &\vec{r}=|\vec{r}|(\hat{i}+m \hat{j}+n \hat{k}) \\ &=12\left(\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{2} \hat{j}-\frac{1}{2} \hat{k}\right) \\ &=6(\sqrt{2} \hat{i}+\hat{j}-\hat{k}) \end{aligned}

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