Question:
Given below are two statements:
Statement I: The angle between the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}-\hat{k}\) is \(\pi/2\)
Statement II: The vector \(\hat{a}\times(\hat{b}\times \hat{c})\) is coplanar with \(\hat{a}\) and \(\hat{b}\)
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements:
Statement I: The angle between the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}-\hat{k}\) is \(\pi/2\)
Statement II: The vector \(\hat{a}\times(\hat{b}\times \hat{c})\) is coplanar with \(\hat{a}\) and \(\hat{b}\)
In the light of the above statements, choose the correct answer from the options given below:
Statement I: The angle between the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}-\hat{k}\) is \(\pi/2\)
Statement II: The vector \(\hat{a}\times(\hat{b}\times \hat{c})\) is coplanar with \(\hat{a}\) and \(\hat{b}\)
In the light of the above statements, choose the correct answer from the options given below:
Updated On: Mar 18, 2024
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
- Statement I is true but Statement II is false
- Statement I is false but Statement II is true
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct answer is(C): Statement I is true but Statement II is false
Was this answer helpful?
0
0
Top Questions on Vectors
- The least positive integral value of \( \alpha \), for which the angle between the vectors \( \alpha \hat{i} - 2\hat{j} + 2\hat{k} \) and \( \alpha \hat{i} + 2\alpha \hat{j} - 2\hat{k} \) is acute, is ______.
- Let \(\vec{a} = \hat{i} + 2\hat{j} + \hat{k}\), \(\vec{b} = 3(\hat{i} - \hat{j} + \hat{k})\). Let \(\vec{c}\) be the vector such that \(\vec{a} \times \vec{c} = \vec{b}\) and \(\vec{a} \cdot \vec{c} = 3\). Then \(\vec{a} \cdot ((\vec{c} \times \vec{b}) - \vec{b} \cdot \vec{c})\) is equal to:
- Let \( A (2, 3, 5) \) and \( C(-3, 4, -2) \) be opposite vertices of a parallelogram \( ABCD \). If the diagonal \( \overrightarrow{BD} = \hat{i} + 2 \hat{j} + 3 \hat{k} \), then the area of the parallelogram is equal to
- Let \( \vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \) and \( \vec{b} = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k} \) be two vectors such that \( |\vec{a}| = 1 \), \( \vec{a} \times \vec{b} = 2 \), and \( |\vec{b}| = 4 \). If \( \vec{c} = 2(\vec{a} \times \vec{b}) - 3\vec{b} \), then the angle between \( \vec{b} \) and \( \vec{c} \) is equal to:
- Consider a vector field \( \vec{F} = (2xz + 3y^2)\hat{y} + 4yz^2\hat{z} \). The closed path (\( \Gamma \): \( A \rightarrow B \rightarrow C \rightarrow D \rightarrow A \)) in the \( z = 0 \) plane is shown in the figure.
\( \oint_\Gamma \vec{F} \cdot d\vec{l} \) denotes the line integral of \( \vec{F} \) along the closed path \( \Gamma \). Which of the following options is/are true?
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
- The surface area of the sphere x2 + y2 + z2 = 9 lying inside the cylinder x2 + y2 = 3y is
- CUET (PG) - 2023
- Surface Area of Cube, Cuboid and Cylinder
- The Ombudsman in a newspaper organisation represents the point of view of the ___.
- CUET (PG) - 2023
- Journalism
- The orthogonal trajectories of the family of curves y = \(ax^3\) is
- The minimum distance of the point (3, 4, 12) from the sphere x2 + y2 + z2 = 1 is
- CUET (PG) - 2023
- Coordinate Geometry
View More Questions