Write a unit vector in the direction of \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\].

Given: \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\]\[\left| \overrightarrow{b} \right| = \sqrt{2^2 + 1^2 + 2^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3\]&there4; Unit vector = \[\frac{\overrightarrow{b}}{\left| \overrightarrow{b} \right|} = \frac{1}{3}\left( 2 \hat{i} + \hat{j} + 2 \hat{k} \right) = \frac{2}{3} \hat{i} + \frac{1}{3} \stackrel\frown{j} + \frac{2}{3} \hat{k}\]

Write a Unit Vector in the Direction of → B = 2 ^ I + ^ J + 2 ^ K . - Mathematics

Question

Write a unit vector in the direction of $\vec{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}$ .

Sum

Solution

Given: $\vec{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}$
$| \vec{b} | = \sqrt{2^{2} + 1^{2} + 2^{2}} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3$
∴ Unit vector = $\frac{\vec{b}}{| \vec{b} |} = \frac{1}{3} (2 \hat{i} + \hat{j} + 2 \hat{k}) = \frac{2}{3} \hat{i} + \frac{1}{3} \overset{⌢}{j} + \frac{2}{3} \hat{k}$

shaalaa.com

Vectors and Their Types

Is there an error in this question or solution?

Q 31 Q 30 Q 32

Chapter 23: Algebra of Vectors - Very Short Answers [Page 76]

APPEARS IN

RD Sharma Mathematics [English] Class 12

Chapter 23 Algebra of Vectors
Very Short Answers | Q 31 | Page 76

Video TutorialsVIEW ALL [2]

view
Video Tutorials For All Subjects
Vectors and Their Types

video tutorial01:01:12
Vectors and Their Types

video tutorial00:11:53

RELATED QUESTIONS

If $\vec{a}$ and $\vec{b}$ denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.

If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin² α + sin² β + sin² γ.

Find the position vector of the mid-point of the line segment AB, where A is the point (3, 4, −2) and B is the point (1, 2, 4).

Find the value of 'p' for which the vectors $3 \hat{i} + 2 \hat{j} + 9 \hat{k}$ and $\hat{i} - 2 p \hat{j} + 3 \hat{k}$ are parallel.

Write a unit vector in the direction of $\vec{P Q}$ , where P and Q are the points (1, 3, 0) and (4, 5, 6) respectively.

In a triangle OAC, if B is the mid-point of side AC and $\vec{O A} = \vec{a}, \vec{O B} = \vec{b}$ , then what is $\vec{O C}$ .

Forces 3 O $\vec{A}$ , 5 O $\vec{B}$ act along OA and OB. If their resultant passes through C on AB, then

If $\vec{a}$ and $\vec{b}$ are non- collinear vectors, find the value of x such that the vectors $\bar{α} = (x - 2) \vec{a} + \vec{b}$ and $\bar{β} = (3 + 2 x) \bar{a} - 2 \bar{b}$ are collinear.

Find a vector in the direction of $\bar{a} = \hat{i} - 2 \hat{j}$ that has magnitude 7 units.

Find the coordinates of the point which is located in the YZ-plane, one unit to the right of the XZ- plane, and six units above the XY-plane.

Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).

If the sum of two unit vectors is itself a unit vector, then the magnitude of their difference is ______.

Dot product of a vector with vectors $3 \hat{i} - 5 \hat{k}, 2 \hat{i} + 7 \hat{j} and \hat{i} + \hat{j} + \hat{k}$ are respectively -1, 6 and 5. Find the vector.

Express the vector $\bar{a} = 5 \hat{i} - 2 \hat{j} + 5 \hat{k}$ as a sum of two vectors such that one is parallel to the vector $\bar{b} = 3 \hat{i} + \hat{k}$ and other is perpendicular to $\bar{b}$ .

Find the acute angle between the curves at their points of intersection, y = x², y = x³.

Let bar"b" = 4hat"i" + 3hat"j" and bar"c" be two vectors perpendicular to each other in the XY-plane. Find the vector in the same plane having projection 1 and 2 along bar"b" and bar"c" respectively.

Find the volume of the parallelopiped spanned by the diagonals of the three faces of a cube of side a that meet at one vertex of the cube.

The vector eqliation of line 2x - 2 = 3y + 1 = 6z - 2 is

The points A(- a, -b), B (0, 0), C(a, b) and D(a² , ab) are ______.

lf $\bar{a}$ , $\bar{b}$ and $\bar{c}$ are unit vectors such that $\bar{a} + \bar{b} + \bar{c} = \bar{0}$ and angle between $\bar{a}$ and $\bar{b}$ is $\frac{π}{3}$ , then $| \bar{a} \times \bar{b} | + | \bar{b} \times \bar{c} | + | \bar{c} \times \bar{a} |$ = ______

Find a vector $\vec{r}$ of magnitude $3 \sqrt{2}$ units which makes an angle of $\frac{π}{4}$ and $\frac{π}{2}$ with y and z-axes, respectively.

The angle between the vectors $\hat{i} - \hat{j}$ and $\hat{j} - \hat{k}$ is ______.

If $\vec{a} = \hat{i} + \hat{j} + 2 \hat{k}$ and $\vec{b} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ , find the unit vector in the direction of $6 \vec{b}$

The formula ${(\vec{a} + \vec{b})}^{2} = {\vec{a}}^{2} + {\vec{b}}^{2} + 2 \vec{a} \times \vec{b}$ is valid for non-zero vectors $\vec{a}$ and $\vec{b}$

Classify the following as scalar and vector quantity.

Velocity

If $\vec{a} \neq \vec{0}, \vec{a} . \vec{b} = \vec{a} . \vec{c}, \vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ , then show that $\vec{b} = \vec{c}$ .

Which of the following measures as vector?

Find $| \vec{a} \times \vec{b} |$ , if $\vec{a} = \hat{i} - 7 \hat{j} + 7 \hat{k}$ and $\vec{b} = 3 \hat{i} - 2 \hat{j} + 2 \hat{k}$

If points P(4, 5, x), Q(3, y, 4) and R(5, 8, 0) are collinear, then the value of x + y is ______.

Unit vector along $\vec{P Q}$ , where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is ______.

Check whether the vectors $2 \hat{i} + 2 \hat{j} + 3 \hat{k}, - 3 \hat{i} + 3 \hat{j} + 2 \hat{k} and 3 \hat{i} + 4 \hat{k}$ form a triangle or not.

In the triangle PQR, $\bar{P Q}$ = $2 \bar{a}$ and $\bar{Q R}$ = $2 \bar{b}$ . The mid-point of PR is M. Find following vectors in terms of $\bar{a}$ and $\bar{b}$ .

(i) $\bar{P R}$ (ii) $\bar{P M}$ (iii) $\bar{Q M}$

In the triangle PQR, $\bar{PQ} = 2 \bar{a} and \bar{QR} = 2 \bar{b}$ . The midpoint of PR is M. Find the following vectors in terms of $\bar{a}$ and $\bar{b}$ :

(i) $\bar{PR}$ (ii) $\bar{PM}$ (iii) $\bar{QM}$

Check whether the vectors $2 \hat{i} + 2 \hat{j} + 3 \hat{k}, - 3 \hat{i} + 3 \hat{j} + 2 \hat{k} and 3 \hat{i} + 4 \hat{k}$ form a triangle or not.

In the triangle PQR, $\bar{P Q}$ = 2 $\bar{a}$ and $\bar{Q R}$ = 2 $\bar{b}$ . The mid-point of PR is M. Find following vectors in terms of $\bar{a}$ and $\bar{b}$ .

$\bar{P R}$
$\bar{P M}$
$\bar{Q M}$

Write a Unit Vector in the Direction of → B = 2 ^ I + ^ J + 2 ^ K . - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Select a course

Write a Unit Vector in the Direction of → B = 2 ^ I + ^ J + 2 ^ K . - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Select a course

Solution