>
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 21, 2024
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
Let
\(\overrightarrow{OP}=\frac{\alpha-1}{\alpha}\hat{i}+\hat{j}+\hat{k},\overrightarrow{OQ}=\hat{i}+\frac{\beta-1}{\beta}\hat{j}+\hat{k}\)
and
\(\overrightarrow{OR}=\hat{i}+\hat{j}+\frac{1}{2}\hat{k}\)
be three vector where α, β ∈ R - {0} and 0 denotes the origin. If
\((\overrightarrow{OP}\times\overrightarrow{OQ}).\overrightarrow{OR}=0\)
and the point (α, β, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.
JEE Advanced - 2024
Mathematics
Vector Algebra
View Solution
Let \[\vec{a} = \hat{i} + \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} - 8\hat{j} + 2\hat{k}, \quad \text{and} \quad \vec{c} = 4\hat{i} + c_2\hat{j} + c_3\hat{k} \]be three vectors such that \[\vec{b} \times \vec{a} = \vec{c} \times \vec{a}.\]If the angle between the vector $\vec{c}$ and the vector $3\hat{i} + 4\hat{j} + \hat{k}$ is $\theta$, then the greatest integer less than or equal to $\tan^2 \theta$ is:
JEE Main - 2024
Mathematics
Vector Algebra
View Solution
Let \( \vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \, \vec{b} = 3\hat{i} + 4\hat{j} - 5\hat{k} \), and a vector \( \vec{c} \) be such that \[ \vec{a} \times (\vec{b} + \vec{c}) + \vec{b} \times \vec{c} = \hat{i} + 8\hat{j} + 13\hat{k}. \] If \( \vec{a} \cdot \vec{c} = 13 \), then \( (24 - \vec{b} \cdot \vec{c}) \) is equal to ______.
JEE Main - 2024
Mathematics
Vector Algebra
View Solution
Let $\vec{a} = 2\hat{i} + \hat{j} - \hat{k}$, $\vec{b} = \left((\vec{a} \times (\hat{i} + \hat{j})) \times \hat{i}\right) \times \hat{i}$. Then the square of the projection of $\vec{a}$ on $\vec{b}$ is:
JEE Main - 2024
Mathematics
Vector Algebra
View Solution
Let $\vec{a} = 6\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{i} + \hat{j}$. If $\vec{c}$ is a vector such that \[ |\vec{c}| \geq 6, \quad \vec{a} \cdot \vec{c} = 6 |\vec{c}|, \quad |\vec{c} - \vec{a}| = 2\sqrt{2} \] and the angle between $\vec{a} \times \vec{b}$ and $\vec{c}$ is $60^\circ$, then $|(\vec{a} \times \vec{b}) \times \vec{c}|$ is equal to:
JEE Main - 2024
Mathematics
Vector Algebra
View Solution
View More Questions
Questions Asked in CUET PG exam
Find out the degree of the differential equation
\(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)
CUET (PG) - 2023
Differential Equations
View Solution
The surface area of the sphere x
2
+ y
2
+ z
2
= 9 lying inside the cylinder x
2
+ y
2
= 3y is
CUET (PG) - 2023
Surface Area of Cube, Cuboid and Cylinder
View Solution
The Ombudsman in a newspaper organisation represents the point of view of the ___.
CUET (PG) - 2023
Journalism
View Solution
The orthogonal trajectories of the family of curves y =
\(ax^3\)
is
CUET (PG) - 2023
Curves
View Solution
The minimum distance of the point (3, 4, 12) from the sphere x
2
+ y
2
+ z
2
= 1 is
CUET (PG) - 2023
Coordinate Geometry
View Solution
View More Questions