The values of x for which the angle between t | vedclass

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

Question

(A) The angle $	heta$ between two vectors $\bar{a}$ and $\bar{b}$ is obtuse if their dot product $\bar{a} \cdot \bar{b} < 0$. Given $\bar{a} = 2x^2 \

Vedclass · Accepted Answer

$0 < x < \frac{1}{2}$

Vedclass · Answer

(A) The angle $	heta$ between two vectors $\bar{a}$ and $\bar{b}$ is obtuse if their dot product $\bar{a} \cdot \bar{b} Given $\bar{a} = 2x^2 \hat{i} + 4x \hat{j} + \hat{k}$ and $\bar{b} = 7 \hat{i} - 2 \hat{j} + x \hat{k}$. Calculating the dot product: $\bar{a} \cdot \bar{b} = (2x^2)(7) + (4x)(-2) + (1)(x) = 14x^2 - 8x + x = 14x^2 - 7x$. For the angle to be obtuse,we require $14x^2 - 7x Dividing by $7$,we get $2x^2 - x The roots of the quadratic equation $x(2x - 1) = 0$ are $x = 0$ and $x = \frac{1}{2}$. Testing the intervals,the inequality $x(2x - 1) Thus,the correct option is $A$.

The values of $x$ for which the angle between the vectors $\bar{a} = 2x^2 \hat{i} + 4x \hat{j} + \hat{k}$ and $\bar{b} = 7 \hat{i} - 2 \hat{j} + x \hat{k}$ is obtuse,are

Similar Questions

If $\hat{a}$ is a unit vector such that $(\bar{x}-\hat{a}) \cdot (\bar{x}+\hat{a}) = 8$,then $|\bar{x}| = $

If $\overrightarrow{A} = 3\hat{i} + \hat{j} + 2\hat{k}$ and $\overrightarrow{B} = 2\hat{i} - 2\hat{j} + 4\hat{k}$ and $\theta$ is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$,then the value of $\sin \theta$ is

If the position vectors of the vertices $A, B$ and $C$ of $\triangle ABC$ are $\hat{i}+2\hat{j}-5\hat{k}$,$-2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+\hat{j}-\hat{k}$ respectively,then $\angle B=$

If the force $\overrightarrow{F} = \hat{i} + 2\hat{j} + 3\hat{k}$ moves a particle from position $\vec{r_1} = \hat{i} + \hat{j} - \hat{k}$ to $\vec{r_2} = 2\hat{i} - \hat{j} + \hat{k},$ then the work done is:

If $|a| = 3$ and $|b| = 4$,then a value of $\lambda$ for which $a + \lambda b$ is perpendicular to $a - \lambda b$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module