Given-the-position-vectors-v-1-2i-2j-and-v-2-2j-a-show-that-the-unit-vector-in-the-direction-of-v-1-v-2-1-5-i-2j-b-Write-down-the-equation-of-the-line-that-contains-the-position-vectors-

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Question Number 48958 by Rio Michael last updated on 30/Nov/18

$$Giventhepositionvectors{v}_1=2\mathit{i}-2\mathit{j}and{v}_2=2\mathit{j}$$$$a)showthattheunitvectorinthedirectionof{v}_1-v_2=\frac{1}{\sqrt{5}}(i-2j)$$$$b)Writedowntheequationofthelinethatcontains$$$$thepositionvectors{v}_{1}and{v}_2$$$$c)Findthecosineoftheanglebetween{v}_{1}and{v}_2$$

Answered by ajfour last updated on 30/Nov/18

$$a){\overline{v}}_1-{\overline{v}}_2=(2\hat{i}-2\hat{j})-2\hat{j}=2\hat{i}-4\hat{j}$$$$so{\hat{v}}_{12},{\hat{v}}_{21}=\pm \frac{({\overline{v}}_1-{\overline{v}}_2)}{\mid {\overline{v}}_1-{\overline{v}}_2\mid }=\pm \frac{1}{\sqrt{5}}(\hat{i}-2\hat{j})$$$$b)\overline{r}=\left({\overline{v}}_{1}or{\overline{v}}_2\right)+\lambda ({\overline{v}}_1-{\overline{v}}_2)$$$$\Rightarrow \overline{r}=2\hat{j}+\lambda (2\hat{i}-4\hat{j})$$$$c)\cos \theta =\frac{{\overline{v}}_1.{\overline{v}}_2}{\mid {\overline{v}}_1\mid \mid {\overline{v}}_2\mid }=\frac{-4}{2\sqrt{2}\times 2}=-\frac{1}{\sqrt{2}}.$$

Commented by Rio Michael last updated on 09/Dec/18

$$siridonotunderstandhowdiditbecome\pm \frac{1}{\sqrt{5}}(i-2j)?$$$$plssimplifymore$$

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