Find the unit vector in the direction of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $\vec{c}$ be the sum of vectors $\vec{a}$ and $\vec{b}$.$\vec{c} = \vec{a} + \vec{b} = (2 \hat{i} - \hat{j} + 2 \hat{k}) + (-\hat{i} + \hat{j}

Vedclass · Accepted Answer

$\frac{1}{\sqrt{26}}(\hat{i}+5 \hat{k})$

Vedclass · Answer

(A) Let $\vec{c}$ be the sum of vectors $\vec{a}$ and $\vec{b}$.$\vec{c} = \vec{a} + \vec{b} = (2 \hat{i} - \hat{j} + 2 \hat{k}) + (-\hat{i} + \hat{j} + 3 \hat{k})$$\vec{c} = (2-1) \hat{i} + (-1+1) \hat{j} + (2+3) \hat{k} = \hat{i} + 0 \hat{j} + 5 \hat{k} = \hat{i} + 5 \hat{k}$Now,calculate the magnitude of $\vec{c}$:$|\vec{c}| = \sqrt{1^2 + 0^2 + 5^2} = \sqrt{1 + 25} = \sqrt{26}$The unit vector in the direction of $\vec{c}$ is given by $\hat{c} = \frac{\vec{c}}{|\vec{c}|}$.$\hat{c} = \frac{\hat{i} + 5 \hat{k}}{\sqrt{26}} = \frac{1}{\sqrt{26}} \hat{i} + \frac{5}{\sqrt{26}} \hat{k}$.

Find the unit vector in the direction of the sum of the vectors $\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=-\hat{i}+\hat{j}+3 \hat{k}$.

Similar Questions

If $\alpha, \beta, \gamma$ are real numbers such that $(\frac{7}{3}+\beta) \hat{i}-\hat{j}+(\alpha+\gamma) \hat{k}=\frac{5}{3}(\alpha \hat{i}+\hat{j}-\hat{k})+\beta(2 \hat{j}+\hat{k})+(\hat{i}+\gamma \hat{j}+3 \hat{k})$, then $5 \alpha-9 \beta+13 \gamma=$

If $ABCD$ is a parallelogram with $AC$ and $BD$ as diagonals,then which of the following is true regarding the vector relationship between the diagonals and sides?

In the given figure (a square),identify the following vectors:
Collinear but not equal

If $a$ is collinear with $b = 3 \hat{i} + 6 \hat{j} + 6 \hat{k}$ and $a \cdot b = 27$,then $|a| =$

In the given figure,which of the vectors are equal?

Vedclass Test Series

Exam Paper Generator

Online Exam Module