Question:
If \(\overrightarrow a,\overrightarrow b,\overrightarrow c\) are three non-coplanar vectors and p,q,r are vectors defined by
\(\overrightarrow p=\frac{\overrightarrow a\times \overrightarrow c}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\) ,\(\overrightarrow q=\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\),\(\overrightarrow r=\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\)then
\((\overrightarrow a+\overrightarrow b).\overrightarrow p+(\overrightarrow b+\overrightarrow c).\overrightarrow q+(\overrightarrow c+\overrightarrow a).\overrightarrow r\) is
If \(\overrightarrow a,\overrightarrow b,\overrightarrow c\) are three non-coplanar vectors and p,q,r are vectors defined by
\(\overrightarrow p=\frac{\overrightarrow a\times \overrightarrow c}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\) ,\(\overrightarrow q=\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\),\(\overrightarrow r=\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\)then
\((\overrightarrow a+\overrightarrow b).\overrightarrow p+(\overrightarrow b+\overrightarrow c).\overrightarrow q+(\overrightarrow c+\overrightarrow a).\overrightarrow r\) is
\(\overrightarrow p=\frac{\overrightarrow a\times \overrightarrow c}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\) ,\(\overrightarrow q=\frac{\overrightarrow c\times \overrightarrow a}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\),\(\overrightarrow r=\frac{\overrightarrow a\times \overrightarrow b}{[\overrightarrow a\overrightarrow b\overrightarrow c]}\)then
\((\overrightarrow a+\overrightarrow b).\overrightarrow p+(\overrightarrow b+\overrightarrow c).\overrightarrow q+(\overrightarrow c+\overrightarrow a).\overrightarrow r\) is
Updated On: Apr 26, 2024
- 0
- 1
- 2
- 3
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct answer is Option (D) : 3
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 KCET exam
- Ten identical cells each emf 2V and internal resistance 1Ω are connected in series with two cells wrongly connected. A resistor of 10Ω is connected to the combination. What is the current through the resistor?
- KCET - 2023
- Cells in Series and in Parallel
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
View More Questions