Write the Component of → B Along → a - Mathematics

प्रश्न

Write the component of $\vec{b}$ along $\vec{a}$

बेरीज

उत्तर

$Component of \vec{b} on \vec{a} is$
${\frac{\vec{a} . \vec{b}}{| a |}} \hat{a} = {\frac{(\vec{a} . \vec{b})}{{| \vec{a} |}^{2}}} \vec{a} = \frac{(\vec{a} . \vec{b}) \vec{a}}{{| \vec{a} |}^{2}}$

shaalaa.com

Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 18 Q 17 Q 19

पाठ 24: Scalar Or Dot Product - very short answer [पृष्ठ ४७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12

पाठ 24 Scalar Or Dot Product
very short answer | Q 18 | पृष्ठ ४७

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

view
व्हिडिओ ट्यूटोरियल For All Subjects
Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors

video tutorial01:46:21
Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors

video tutorial01:03:03

संबंधित प्रश्‍न

If $\vec{a}$ and $\vec{b}$ are two unit vectors such that $\vec{a} + \vec{b}$ is also a unit vector, then find the angle between $\vec{a}$ and $\vec{b}$

Vectors $\vec{a}, \vec{b} and \vec{c}$ are such that $\vec{a} + \vec{b} + \vec{c} = 0 and | \vec{a} | = 3, | \vec{b} | = 5 and | \vec{c} | = 7$ Find the angle between $\vec{a} and \vec{b}$

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$ , then write the value of $\vec{a} . \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}$ .

The scalar product of the vector $\vec{a} = \hat{i} + \hat{j} + \hat{k}$ with a unit vector along the sum of vectors $\vec{b} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k} and \vec{c} = λ \hat{i} + 2 \hat{j} + 3 \hat{k}$ is equal to one. Find the value of λ and hence, find the unit vector along $\vec{b} + \vec{c}$

Show that each of the given three vectors is a unit vector:

$\frac{1}{7} (2 \hat{i} + 3 \hat{j} + 6 \hat{j}), \frac{1}{7} (3 \hat{i} - 6 \hat{j} + 2 \hat{k}), \frac{1}{7} (6 \hat{i} + 2 \hat{j} - 3 \hat{k})$

Also, show that they are mutually perpendicular to each other.

The scalar product of the vector $\hat{i} + \hat{j} + \hat{k}$ with a unit vector along the sum of vectors $2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ and $λ \hat{i} + 2 \hat{j} + 3 \hat{k}$ is equal to one. Find the value of $λ$ .

For what value of λ are the vectors $\vec{a} and \vec{b}$ perpendicular to each other if $\vec{a} = λ \hat{i} + 2 \hat{j} + \hat{k} and \vec{b} = 4 \hat{i} - 9 \hat{j} + 2 \hat{k}$

$If \vec{a} = \hat{i} - \hat{j} and \vec{b} = - \hat{j} + 2 \hat{k}, find (\vec{a} - 2 \vec{b}) \cdot (\vec{a} + \vec{b}) .$

What is the angle between vectors $\vec{a} and \vec{b}$ with magnitudes 2 and $\sqrt{3}$ respectively? Given $\vec{a} . \vec{b} = \sqrt{3} .$

If $\vec{a} and \vec{b}$ are vectors of equal magnitude, write the value of $(\vec{a} + \vec{b}) . (\vec{a} - \vec{b}) .$

For any two vectors $\vec{a} and \vec{b}$ write when $| \vec{a} + \vec{b} | = | \vec{a} - \vec{b} |$ holds.

If $\hat{a}, \hat{b}$ are unit vectors such that $\hat{a} + \hat{b}$ is a unit vector, write the value of $| \hat{a} - \hat{b} | .$

If $| \vec{a} | = 2, | \vec{b} | = 5 and \vec{a} . \vec{b} = 2, find | \vec{a} - \vec{b} | .$

Write a vector satisfying $\vec{a} . \hat{i} = \vec{a} . (\hat{i} + \hat{j}) = \vec{a} . (\hat{i} + \hat{j} + \hat{k}) = 1 .$

If $\vec{a} and \vec{b}$ are unit vectors, find the angle between $\vec{a} + \vec{b} and \vec{a} - \vec{b} .$

If $\vec{a}, \vec{b} and \vec{c}$ are mutually perpendicular unit vectors, write the value of $| \vec{a} + \vec{b} + \vec{c} | .$

For what value of λ are the vectors $\vec{a} = 2 \hat{i} + λ \hat{j} + \hat{k} and \vec{b} = \hat{i} - 2 \hat{j} + 3 \hat{k}$ perpendicular to each other?

Write the value of p for which $\vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} and \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k}$ are parallel vectors .

Find the value of λ if the vectors $2 \hat{i} + λ \hat{j} + 3 \hat{k} and 3 \hat{i} + 2 \hat{j} - 4 \hat{k}$ are perpendicular to each other.

If $| \vec{a} | = 2, | \vec{b} | = 3 and \vec{a} \cdot \vec{b} = 3,$ find the projection of $\vec{b} on \vec{a}$

Write the angle between two vectors $\vec{a} and \vec{b}$ with magnitudes $\sqrt{3}$ and 2 respectively if $\vec{a} \cdot \vec{b} = \sqrt{6} .$

Write the projection of the vector $\hat{i} + 3 \hat{j} + 7 \hat{k}$ on the vector $2 \hat{i} - 3 \hat{j} + 6 \hat{k}$

Write the value of λ so that the vectors $\vec{a} = 2 \hat{i} + λ \hat{j} + \hat{k} and \vec{b} = \hat{i} - 2 \hat{j} + 3 \hat{k}$ are perpendicular to each other.

If $\vec{a}$ and $\vec{b}$ are perpendicular vectors, $| \vec{a} + \vec{b} | = 13$ and $| \vec{a} | = 5$ find the value of $| \vec{b} |$

If $\vec{a}$ and $\vec{b}$ are two unit vectors such that $\vec{a} + \vec{b}$ is also a unit vector, then find the angle between $\vec{a}$ and $\vec{b}$

Show that the vectors $\vec{a,} \vec{b,} \vec{c}$ are coplanar if and only if $\vec{a} + \vec{b}$ , $\vec{b} + \vec{c}$ and $\vec{c} + \vec{a}$ are coplanar.

Let $\vec{a} = \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $\vec{b} = 3 \hat{i} - j + 2 \hat{k}$ be two vectors. Show that the vectors $(\vec{a} + \vec{b})$ and $(\vec{a} - \vec{b})$ are perpendicular to each other.

If two vectors $\vec{a}$ and $\vec{b}$ are such that $| \vec{a} |$ = 2, $| \vec{b} |$ = 3 and $\vec{a} . \vec{b}$ = 4, then $| \vec{a} - 2 \vec{b} |$ is equal to ______.

If $\vec{a}, \vec{b}, \vec{c}$ are three non-zero unequal vectors such that $\vec{a} . \vec{b} = \vec{a} . \vec{c}$ , then find the angle between $\vec{a}$ and $\vec{b} - \vec{c}$ .

If $\vec{a} . \hat{i} = \vec{a} . (\hat{i} + \hat{j}) = \vec{a} . (\hat{i} + \hat{j} + \hat{k})$ = 1, then $\vec{a}$ is ______.

If $\vec{a} = 2 \hat{i} + \hat{j} + 2 \hat{k}$ and $\vec{b} = 5 \hat{i} - 3 \hat{j} + \hat{k}$ , find the projection of $\vec{b}$ on $\vec{a}$ .

Write the Component of → B Along → a - Mathematics

Advertisements

Advertisements

प्रश्न

उत्तर

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Select a course

Write the Component of → B Along → a - Mathematics

Advertisements

Advertisements

प्रश्न

उत्तरShow Solution

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Select a course

उत्तर