Question
If the angle between two non-zero vectors $\vec{a}$ and $\vec{b}$ is $\theta$, then $\cos \theta=$ ___________ .
✓
Answer
$\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Fill in the blank.
_________ matrix is both symmetric and skew symmetric matrix.
_________ matrix is both symmetric and skew symmetric matrix.
Fill in the blanks.
If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9, P (X = 3), then p = _________.
If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9, P (X = 3), then p = _________.
Fill in the blank.
The negative of a matrix is obtained by multiplying it by _________.
The negative of a matrix is obtained by multiplying it by _________.
Fill in the blanks.
If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
→If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
Fill in the blanks.
If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
→If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
The number of arbitrary constants present in the general solution of any differential equation of order three will be ____________ .
If $P ( A )=\frac{1}{2}, P ( B )=0$ then $P ( A \mid B )$ is _____________ .
→Fill in the blanks.
The solution of $(1+\text{x})^2\frac{\text{dy}}{\text{dx}}+2\text{xy}-4\text{x}^2=0$ is _________.
→The solution of $(1+\text{x})^2\frac{\text{dy}}{\text{dx}}+2\text{xy}-4\text{x}^2=0$ is _________.
Ajay cut two circular pieces of cardboard and placed one upon other as shown in figure. One of the circle represents the equation $(x - 1)^2+ y^2= 1$, while other circle represents the equation $x^2+ y^2= 1.$
Based on the above information, answer the following questions.
→Based on the above information, answer the following questions.
- Both the circular pieces of cardboard meet each other at
- $\text{x}=1$
- $\text{x}=\frac{1}{2}$
- $\text{x}=\frac{1}{3}$
- $\text{x}=\frac{1}{4}$
- Graph of given two curves can be drawn as.
- None of these
- Value of $\int\limits_{0}^{\frac{1}{2}}\sqrt{1-(\text{x}-1)^2}\text{dx}$ is.
- $\frac{\pi}{6}-\frac{\sqrt{3}}{8}$
- $\frac{\pi}{6}+\frac{\sqrt{3}}{8}$
- $\frac{\pi}{2}+\frac{\sqrt{3}}{4}$
- $\frac{\pi}{2}-\frac{\sqrt{3}}{4}$
- Value of $\int\limits_{\frac{1}{2}}^{1}\sqrt{1-\text{x}^2}\text{dx}$ is.
- $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$
- $\frac{\pi}{6}+\frac{\sqrt{3}}{8}$
- $\frac{\pi}{6}-\frac{\sqrt{3}}{8}$
- $\frac{\pi}{2}-\frac{\sqrt{3}}{4}$
- Area of hidden portion of lower circle is.
- $\bigg(\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\bigg)\text{ sq.units}$
- $\bigg(\frac{\pi}{3}-\frac{\sqrt{3}}{8}\bigg)\text{ sq.units}$
- $\bigg(\frac{\pi}{3}+\frac{\sqrt{3}}{8}\bigg)\text{ sq.units}$
- $\bigg(\frac{2\pi}{3}-\frac{\sqrt{3}}{2}\bigg)\text{ sq.units}$
Fill in the blanks.
A corner point of a feasible region is a point in the region which is the _________ of two boundary lines.
A corner point of a feasible region is a point in the region which is the _________ of two boundary lines.