Question

Write two different vectors having same direction.

Answer 1

Answer-


Let two vector be

P and q.


→p = 2i+3j+6k +λ(i+3j+3k)

→q= 3i+2j+3k+μ(3i+8j+12k)

put λ=1

and μ=2.

Answer 2

$\bigstar$ Solution:

Consider $\vec{p} = ( \hat{i} + \hat{j} + \hat{k})$ and $\vec{q}=(2\hat{i} + 2\hat{j} + 2\hat{k})$

The direction cosines of $\vec{p}$ are given by,

$l=\frac{1}{\sqrt{1^{2} + 1^{2} + 1^{2}} } = \frac{1}{\sqrt{3} }, \: m = \frac{1}{1^{2} + 1^{2} + 1^{2}} = \frac{1}{\sqrt{3} }, \; and \: n = \frac{1}{1^{2} + 1^{2} + 1^{2}} = \frac{1}{\sqrt{3} }$

The direction cosines of $\vec{q}$ are given by,

$l=\frac{2}{2^{2} + 2^{2} + 2^{2}}= \frac{2}{\sqrt[2]{3} } = \frac{1}{\sqrt{3} }, \:m=\frac{2}{2^{2} + 2^{2} + 2^{2}}= \frac{2}{\sqrt[2]{3} } = \frac{1}{\sqrt{3} }, \: n= \frac{2}{2^{2} + 2^{2} + 2^{2}} =\frac{2}{\sqrt[2]{3} } = \frac{1}{\sqrt{3} }$$\rule{300}{1.5}$

Consider $\vec{p} = ( \hat{i} + \hat{j} + \hat{k})$ and $\vec{q}=(2\hat{i} + 2\hat{j} + 2\hat{k})$

The direction cosines of $\vec{p}$ are given by,

$l=\frac{1}{\sqrt{1^{2} + 1^{2} + 1^{2}} } = \frac{1}{\sqrt{3} }, \: m = \frac{1}{1^{2} + 1^{2} + 1^{2}} = \frac{1}{\sqrt{3} }, \; and \: n = \frac{1}{1^{2} + 1^{2} + 1^{2}} = \frac{1}{\sqrt{3} }$

The direction cosines of $\vec{q}$ are given by,

$l=\frac{2}{2^{2} + 2^{2} + 2^{2}}= \frac{2}{\sqrt[2]{3} } = \frac{1}{\sqrt{3} }, \:m=\frac{2}{2^{2} + 2^{2} + 2^{2}}= \frac{2}{\sqrt[2]{3} } = \frac{1}{\sqrt{3} }, \: n= \frac{2}{2^{2} + 2^{2} + 2^{2}} =\frac{2}{\sqrt[2]{3} } = \frac{1}{\sqrt{3} }$$\rule{300}{1.5}$