The value of x for which the angle between th | vedclass

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

Question

(D) Let $\vec{a} = x\hat{i} - 3\hat{j} - \hat{k}$ and $\vec{b} = 2x\hat{i} + x\hat{j} - \hat{k}$.Condition $1$: The angle between $\vec{a}$ and $\vec{

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Let $\vec{a} = x\hat{i} - 3\hat{j} - \hat{k}$ and $\vec{b} = 2x\hat{i} + x\hat{j} - \hat{k}$.Condition $1$: The angle between $\vec{a}$ and $\vec{b}$ is acute,so $\vec{a} \cdot \vec{b} > 0$.$\vec{a} \cdot \vec{b} = (x)(2x) + (-3)(x) + (-1)(-1) = 2x^2 - 3x + 1 > 0$.Solving $2x^2 - 3x + 1 > 0$,we get $(2x - 1)(x - 1) > 0$,which implies $x  1$.Condition $2$: The angle between $\vec{b}$ and the $y$-axis (unit vector $\hat{j}$) is obtuse,so $\vec{b} \cdot \hat{j} $\vec{b} \cdot \hat{j} = (2x\hat{i} + x\hat{j} - \hat{k}) \cdot (0\hat{i} + 1\hat{j} + 0\hat{k}) = x Combining both conditions: $x  1$).The intersection is $x Since none of the options match $x < 0$,the correct answer is $D$.

The value of $x$ for which the angle between the vectors $\vec{a} = x\hat{i} - 3\hat{j} - \hat{k}$ and $\vec{b} = 2x\hat{i} + x\hat{j} - \hat{k}$ is acute,and the angle between the vector $\vec{b}$ and the $y$-axis (axis of ordinate) is obtuse,are:

Similar Questions

The horizontal force and the force inclined at an angle $60^\circ$ with the vertical,whose resultant is in the vertical direction with a magnitude of $P \ kg$,are:

Let $\vec{r}$ be a vector in the plane of $\hat{i} - 2\hat{j} + \hat{k}$ and $\hat{i} - \hat{j} - \hat{k}$ such that $\vec{r} \cdot (\hat{i} + \hat{j}) + 2 = 0$ and the length of the projection of $\vec{r}$ on $\hat{i} - \hat{j}$ is $4\sqrt{2}$. Then,the magnitude of vector $\vec{r}$ is:

If $a, b, c$ and $r$ are vectors such that $a$ is not perpendicular to $b$,$r \times b = c \times b$ and $r \cdot a = 0$,then $r =$

If $a \times r = b + \lambda a$ and $a \cdot r = 3,$ where $a = 2i + j - k$ and $b = -i - 2j + k,$ then $r$ and $\lambda$ are equal to

Classify the following as scalar or vector quantities:
Work done

Vedclass Test Series

Exam Paper Generator

Online Exam Module