Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
MCQ
If the angle between the vectors $\text{x}\hat{\text{i}}+3\hat{\text{j}}-7\hat{\text{k}}$ and $\text{x}\hat{\text{i}}-\text{x}\hat{\text{j}}+4\hat{\text{k}}$ is acute, then x lies in the interval:
  • A
    (-4, 7)
  • B
    [-4, 7]
  • ✓
    R - [-4, 7]
  • D
    R - (4, 7)
✓

Answer

Correct option: C.
R - [-4, 7]
Let $\theta$ be the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

$\cos\theta=\frac{\vec{\text{a}}.\vec{\text{b}}}{|\vec{\text{a}}|\big|\vec{\text{b}}\big|}=\frac{\text{x}^2-3\text{x}-28}{\sqrt{\text{x}^2+3^2+49}\sqrt{\text{x}^2+\text{x}^2+4^2}}$

For $\theta$ to be acute,

$\cos\theta>0$

$\Rightarrow\text{x}^2-3\text{x}-28>0$

$\Rightarrow(\text{x}-7)(\text{x}+4)>0$

$\Rightarrow\text{x}\in(-\infty,-4)\cup(7,\infty)$

$\Rightarrow\text{x}\in\text{R}-[-4,7]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from VECTOR ALGEBRA→VECTOR ALGEBRA — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }\\{\sin \alpha }&{\cos \alpha }\end{array}} \right]$and $B = \left[ {\begin{array}{*{20}{c}}{\cos \beta }&{ - \sin \beta }\\{\sin \beta }&{\cos \beta }\end{array}} \right]$, then the correct relation is
→
The minimum value of $z=2 x+4 y$ subject to constraints $x+2 y \geq 10,3 x+y \geq 10, x \geq 0,$ $y \geq 0$ is $....$
→
Choose the correct answer from the given four options. Let $f : R \rightarrow R$ be the functions defined by $f(x) = x^3 + 5.$ Then $f^{-1}(x)$ is :
→
If the domain and range of $f(x){ = ^{9 - x}}{C_{x - 1}}$ contains $m$ and $n$ elements respectively, then 
→
Choose the correct answer from the given four options.If $\tan^{-1}\text{x}+\tan^{-1}\text{y}=\frac{4\pi}{5},$ then $\cot^{-1}\text{x}+\cot^{-1}\text{y}$ equals to:
→
If $A$ is a square matrix of order 3 and $|A|=6$, then the value of $|\operatorname{adj} A |$ is:
→
Number of binary operations on the set $\{a, b\}$ are:
→
If $I = {\kern 1pt} \int\limits_0^{\frac{\pi }{6}} {\frac{{\cos x}}{x}dx,J = \int\limits_{\frac{\pi }{3}}^{\frac{\pi }{2}} {\frac{{\cos x}}{x}dx.} } $ Which of the following is CORRECT ?
→
The normal to the curve $x^2=4 y$ passing through $(1,2)$ is:
→
The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If 

$S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2}, \frac{3}{4}\right),\left(\frac{1}{4},-\frac{1}{4}\right),\left(\frac{1}{8}, \frac{1}{4}\right)\right\},$ then the number of point(s) in $S$ lying inside the smaller part is

→