Types of Vector

Convert the vector $\overrightarrow{r}=3\stackrel{\wedge }{i}+2\stackrel{\wedge }{j}$ into a unit vector.

Calculate the vector sum of two unit vectors.

If P+Q​+R=0 and out of these, two vectors are equal in magnitude and the third vector has magnitude 2​ times that of these two vectors, then angles among the three vectors are;

Which of the following forces do not cause the rotation. Suppose the rotation is considered inside the body's axis or the centroid axis of the body.

 If A is any vector with Ai + Bj + Ck, then what is the y-axis component of the vector?

Which of the following forces do not cause the rotation. Suppose the rotation is considered inside the body's axis or the centroid axis of the body?

 For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents:

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are two mutually perpendicular vectors. Their dot product remains the same when the magnitude of $\overrightarrow{A}$ becomes three times its previous value.

Define Localised Vector and give one example.

Define free vector and give one example.

The minimum number of unequal forces whose vector sum can be zero is

The unit vector $\left(a\hat{\mathrm{i}}+b\hat{\mathrm{j}}\right)$ is perpendicular to $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right).$ The value of ${}^{\text{'}}b^{\text{'}}$ is

The position vector of a particle is $\overrightarrow{r}=\left(a\cos \omega t\right)\hat{i}+\left(a\sin \omega t\right)\hat{j}$. The velocity vector of the particle is:

Select the correct alternative. The coordinates of a particle moving in a plane are given by $x=a \cos pt$ and $y=b \sin pt$ , where $a, b$ and $p$are positive constants of appropriate dimensions. Then:

The coordinates of a particle at time $t$ are $x=2t+4t^2$ and $y=5t$, where $x$ and $y$ are in metre and $t$ is in second. The acceleration of the particle at $t=5 s$ is :

A unit vector is represented as $\left(0.8\hat{\mathrm{i}}+b\hat{\mathrm{j}}+0.4\hat{\mathrm{k}}\right)$. The value of $b$ must be,

The value of x for which $x.\left(\hat{\text{i}}+\hat{\text{j}}+\hat{k}\right)$ is a unit vector is 

Find the value of $a$, if the vectors $\stackrel{\wedge }{i}-2\stackrel{\wedge }{j}+\stackrel{\wedge }{k}, a\stackrel{\wedge }{i}-5\stackrel{\wedge }{j}+3\stackrel{\wedge }{k}$and $5\stackrel{\wedge }{i}-9\stackrel{\wedge }{j}+4\stackrel{\wedge }{k}$ are coplanar.
 

A unit vector is represented as $\left(0.8\hat{\mathrm{i}}+b\hat{\mathrm{j}}+0.4\hat{\mathrm{k}}\right)$. The value of $b$ must be,

Find the value of $p$, if the vectors $\stackrel{\wedge }{i}-2\stackrel{\wedge }{j}+\stackrel{\wedge }{k} , 2\stackrel{\wedge }{i} - 5\stackrel{\wedge }{j}+p\stackrel{\wedge }{k}$and $5\stackrel{\wedge }{j}- 9\stackrel{\wedge }{j} +4\stackrel{\wedge }{k}$ are coplanar.