>
Exams
>
Mathematics
>
Vector Algebra
>
vec i cdot vec i
Question:
\(\vec i\cdot\vec i=\) ?
Show Hint
$\vec i\cdot\vec i=\vec j\cdot\vec j=\vec k\cdot\vec k=1$; mixed pairs are \(0\).
Bihar Board XII - 2023
Bihar Board XII
Updated On:
Oct 17, 2025
\(0\)
\(1\)
\(-1\)
\(\vec j\)
Show Solution
Verified By Collegedunia
The Correct Option is
B
Solution and Explanation
Unit vectors have length \(1\) and are mutually perpendicular. Dot product of a vector with itself equals the square of its length: \[ \vec i\cdot\vec i=\|\vec i\|^{2}=1^{2}=1. \]
Download Solution in PDF
Was this answer helpful?
0
0
Top Bihar Board XII Mathematics Questions
\(\frac{d}{dx} \left(\sec^2 x - \tan^2 x\right)\)
Bihar Board XII - 2025
Mathematics
Derivatives
View Solution
\(\frac{d}{dx} \left( e^{2x} + 2e^x \right)\)
Bihar Board XII - 2025
Mathematics
Limits
View Solution
\(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)
Bihar Board XII - 2025
Mathematics
Limits
View Solution
\(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
Bihar Board XII - 2025
Mathematics
Inverse Trigonometric Functions
View Solution
\(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
Bihar Board XII - 2025
Mathematics
Differentiation
View Solution
View More Questions
Top Bihar Board XII Vector Algebra Questions
Find the magnitude of the vector
\[ \left| \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \right|. \]
Bihar Board XII - 2025
Mathematics
Vector Algebra
View Solution
Find the square of the vector
\[ (4\mathbf{i} + 3\mathbf{j})^2. \]
Bihar Board XII - 2025
Mathematics
Vector Algebra
View Solution
Find the dot product of the vectors
\[ (7\mathbf{i} - 8\mathbf{j} + 9\mathbf{k}) \cdot (\mathbf{i} - \mathbf{j} + \mathbf{k}). \]
Bihar Board XII - 2025
Mathematics
Vector Algebra
View Solution
Evaluate the following expression:
\[ \mathbf{i} \cdot \mathbf{i} + \mathbf{i} \cdot \mathbf{j} + \mathbf{j} \cdot \mathbf{j} + \mathbf{j} \cdot \mathbf{k} + \mathbf{k} \cdot \mathbf{k} \]
Bihar Board XII - 2025
Mathematics
Vector Algebra
View Solution
Find the dot product of the vectors
\[ (11\mathbf{i} + \mathbf{j} + \mathbf{k}) \cdot (\mathbf{i} + \mathbf{j} + 11\mathbf{k}). \]
Bihar Board XII - 2025
Mathematics
Vector Algebra
View Solution
View More Questions
Top Bihar Board XII Questions
Which metal was first used by humans?
Bihar Board XII - 2025
History of Science & Technology in India
View Solution
Where is the Harappan site called Shortughai located?
Bihar Board XII - 2025
Indus Valley Civilization Art and Sculpture
View Solution
Where has the evidence of dockyard been found from Indus Valley Civilization?
Bihar Board XII - 2025
Indus Valley Civilization Art and Sculpture
View Solution
Which is referred to as Meluhha in Mesopotamian texts?
Bihar Board XII - 2025
Ancient Civilizations and their Contributions
View Solution
Where have miniature pots of faience probably used as perfume bottles been found?
Bihar Board XII - 2025
Indus Valley Civilization Art and Sculpture
View Solution
View More Questions