For all real x,for what value of c does the a | vedclass

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

Question

(C) Let the two vectors be $\vec{a} = cx\hat{i} - 6\hat{j} + 3\hat{k}$ and $\vec{b} = x\hat{i} + 2\hat{j} + 2cx\hat{k}$.For the angle between the vect

Vedclass · Accepted Answer

$-4/3 < c < 0$

Vedclass · Answer

(C) Let the two vectors be $\vec{a} = cx\hat{i} - 6\hat{j} + 3\hat{k}$ and $\vec{b} = x\hat{i} + 2\hat{j} + 2cx\hat{k}$.For the angle between the vectors to be obtuse,their dot product must be negative,i.e.,$\vec{a} \cdot \vec{b} $(cx\hat{i} - 6\hat{j} + 3\hat{k}) \cdot (x\hat{i} + 2\hat{j} + 2cx\hat{k}) $cx^2 - 12 + 6cx^2 $cx^2 + 6cx^2 - 12 Wait,re-evaluating the dot product: $(cx)(x) + (-6)(2) + (3)(2cx) = cx^2 - 12 + 6cx So,$cx^2 + 6cx - 12 For a quadratic expression $Ax^2 + Bx + C Here,$A = c The discriminant $D = (6c)^2 - 4(c)(-12) $36c^2 + 48c Divide by $12$: $3c^2 + 4c $c(3c + 4) This inequality holds when $-4/3 Since we also require $c < 0$,the intersection is $-4/3 < c < 0$.

For all real $x$,for what value of $c$ does the angle between the vectors $cx\hat{i} - 6\hat{j} + 3\hat{k}$ and $x\hat{i} + 2\hat{j} + 2cx\hat{k}$ be an obtuse angle?

Similar Questions

If $\overline{e_1}, \overline{e_2}$ are two non-collinear unit vectors such that $|\overline{e_1}+\overline{e_2}|=\sqrt{3}$,then $(2 \overline{e_1}-5 \overline{e_2}) \cdot (3 \overline{e_1}+\overline{e_2}) = $

The magnitude of vectors $\vec{a}$ and $\vec{b}$ are $1$ and $2$ respectively,and $\vec{a} \cdot \vec{b} = 1$. Then,the angle between the two vectors $\vec{a}$ and $\vec{b}$ is . . . . . . .

$A$ particle acted on by constant forces $4i + j - 3k$ and $3i + j - k$ is displaced from the point $i + 2j + 3k$ to the point $5i + 4j + k$. The total work done by the force is ............... $unit$.

If the vectors $\bar{a}=\hat{i}-\hat{j}+2\hat{k}$,$\bar{b}=2\hat{i}+4\hat{j}+\hat{k}$ and $\bar{c}=m\hat{i}+\hat{j}+n\hat{k}$ are mutually perpendicular,then $(m, n)$ is

Let $a, b$ and $c$ be unit vectors such that $a$ is perpendicular to the plane containing $b$ and $c$ and the angle between $b$ and $c$ is $\frac{\pi}{3}$. Then,$|a+b+c|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module