>
Exams
>
Mathematics
>
Vector Algebra
>
for what value s of k the set of vectors 1 k 5 1 3
Question:
For what value(s) of k the set of vectors {(1, k, 5), (1, -3, 2), (2, -1, 1)} form a basis in R
3
?
CUET (PG) - 2023
CUET (PG)
Updated On:
Mar 12, 2025
k≠
\(\frac{-10}{3}\)
k=-8
k≠8
k≠-8
Hide Solution
Verified By Collegedunia
The Correct Option is
D
Solution and Explanation
The correct answer is(D): k≠-8
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Vector Algebra
If \( \mathbf{a} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} \), find \( \mathbf{a} \cdot \mathbf{b} \) (the dot product).
MHT CET - 2025
Mathematics
Vector Algebra
View Solution
Given that \( \vec{a} \parallel \vec{b} \), \( \vec{a} \cdot \vec{b} = \frac{49}{2} \), and \( |\vec{a}| = 7 \), find \( |\vec{b}| \).
KEAM - 2025
Mathematics
Vector Algebra
View Solution
Let $ \vec{a} $ and $ \vec{b} $ be the vectors of the same magnitude such that
$ \frac{| \vec{a} + \vec{b} | + | \vec{a} - \vec{b} |}{| \vec{a} + \vec{b} | - | \vec{a} - \vec{b} |} = \sqrt{2} + 1. \quad \text{Then } \frac{| \vec{a} + \vec{b} |^2}{| \vec{a} |^2} \text{ is:} $
JEE Main - 2025
Mathematics
Vector Algebra
View Solution
If \( \mathbf{a} = \frac{1}{\sqrt{10}} (4\hat{i} - 3\hat{j} + \hat{k}) \) and \( \mathbf{b} = \frac{1}{5} (\hat{i} + 2\hat{j} + 2\hat{k}) \), then the value of \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]
MHT CET - 2025
Mathematics
Vector Algebra
View Solution
Given that \( |\mathbf{a} + \mathbf{b}| = \frac{\sqrt{14}}{2} \), where \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, find the value of \( |\mathbf{a} + \mathbf{b}|^2 - |\mathbf{a} - \mathbf{b}|^2 \).
KEAM - 2025
Mathematics
Vector Algebra
View Solution
View More Questions
Questions Asked in CUET PG exam
What is the antonym of eradicate?
CUET (PG) - 2025
Antonyms
View Solution
Who was the first Secretary-General of the UN?
CUET (PG) - 2025
United Nations and its Organizations
View Solution
What is the correct verb form: He, as well as his friends, ?
CUET (PG) - 2025
Verbs
View Solution
Which preposition is correct: Chanakya lived ?
CUET (PG) - 2025
Prepositions
View Solution
Identify the possessive noun: My office car is parked elsewhere.
CUET (PG) - 2025
Nouns
View Solution
View More Questions