If vec{a} is a non-zero vector of modulus |ve | vedclass

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

Question

(C) vector $\vec{v}$ is a unit vector if its magnitude is $1$,i.e.,$|\vec{v}| = 1$. Given that $m\vec{a}$ is a unit vector,we have $|m\vec{a}| = 1$. U

Vedclass · Accepted Answer

$m = \frac{1}{|\vec{a}|}$

Vedclass · Answer

(C) vector $\vec{v}$ is a unit vector if its magnitude is $1$,i.e.,$|\vec{v}| = 1$. Given that $m\vec{a}$ is a unit vector,we have $|m\vec{a}| = 1$. Using the property of the modulus of a scalar multiple of a vector,$|m\vec{a}| = |m| |\vec{a}|$. Therefore,$|m| |\vec{a}| = 1$. Since $m$ is a non-zero scalar,we can write $|m| = \frac{1}{|\vec{a}|}$. Assuming $m$ is positive,$m = \frac{1}{|\vec{a}|}$. Thus,option $(C)$ is the correct condition.

If $\vec{a}$ is a non-zero vector of modulus $|\vec{a}|$ and $m$ is a non-zero scalar,then $m\vec{a}$ is a unit vector if:

Similar Questions

$A$ line segment $PQ$ has the length $63$ and direction ratios $(3, -2, 6)$. If this line makes an obtuse angle with the $X$-axis,then the components of the vector $\vec{PQ}$ are

If $a = 2i + 5j$ and $b = 2i - j,$ then the unit vector along $a + b$ will be

If $a, b, c$ are three linearly independent vectors and there exists a non-zero scalar triad $(l, m, n)$ such that $l(3a + 2b + c) + m(2a + 2b + 3c) + n(a + 2b + 5c) = 0$, then:

If $\overline{r} = -4 \hat{i} - 6 \hat{j} - 2 \hat{k}$ is a linear combination of the vectors $\overline{a} = -\hat{i} - 4 \hat{j} + 3 \hat{k}$ and $\overline{b} = -8 \hat{i} - \hat{j} + 3 \hat{k}$,then which of the following is true?

Classify the following physical quantity as a scalar or a vector:
$10 \, g/cm^3$

Vedclass Test Series

Exam Paper Generator

Online Exam Module