The angle between the lines vec{r}=(2 hat{i}- | vedclass

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

Question

(A) The given lines are in the form $\vec{r} = \vec{a} + \lambda \vec{b}$.Comparing the given equations,the direction vectors are $\vec{b_1} = \hat{i}

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(A) The given lines are in the form $\vec{r} = \vec{a} + \lambda \vec{b}$.Comparing the given equations,the direction vectors are $\vec{b_1} = \hat{i} + 4 \hat{j} + 3 \hat{k}$ and $\vec{b_2} = \hat{i} + 2 \hat{j} - 3 \hat{k}$.The angle $	heta$ between two lines with direction vectors $\vec{b_1}$ and $\vec{b_2}$ is given by $\cos 	heta = \frac{|\vec{b_1} \cdot \vec{b_2}|}{|\vec{b_1}| |\vec{b_2}|}$.Calculating the dot product: $\vec{b_1} \cdot \vec{b_2} = (1)(1) + (4)(2) + (3)(-3) = 1 + 8 - 9 = 0$.Since the dot product is $0$,the angle $	heta$ is $\frac{\pi}{2}$.

The angle between the lines $\vec{r}=(2 \hat{i}-3 \hat{j}+\hat{k})+\lambda(\hat{i}+4 \hat{j}+3 \hat{k})$ and $\vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$ is

Similar Questions

The number of molecules in $16 \ g$ of methane is

At a certain temperature,the equilibrium constant $K_c$ is $0.25$ for the reaction:
$A_{2(g)} + B_{2(g)} \rightleftharpoons C_{2(g)} + D_{2(g)}$
If we take $1 \ mol$ of each of the four gases in a $10 \ L$ container,what would be the equilibrium concentration of $A_{2(g)}$ (in $M$)?

Which one of the following metallic hydroxides does not dissolve in sodium hydroxide solution?

The radius of ${}_{52}Te^{125}$ nucleus is $6 \text{ fermi}$. The radius of ${}_{13}Al^{27}$ nucleus in meters is

What is the major product of the following reaction?

Vedclass Test Series

Exam Paper Generator

Online Exam Module