Let \(\vec a =3î + ĵ -2k̂\), \(\vec b =4 î + ĵ +7 k̂\) and \(\vec c =î -3 ĵ +4 k̂\) be 3 vectors. If a vector \(\vec p\) satisfies \(\vec p_x \vec b=\vec c_x\vec b\) and \(\vec p_x\vec a = 0\) then \(\vec p.( î - ĵ - k̂ )\) is equal to
- 32
- 23
- 16
- 61
The Correct Option is A
Solution and Explanation
Top Questions on Vector Algebra
- Let \(\vec{p}=2\hat{i}+\hat{j}+3\hat{k}\) and \(\vec{q}=\hat{i}-\hat{j}+\hat{k}\). If for some real numbers α, β and γ we have
\(15\hat{i}+10\hat{j}+6\hat{k}=α(2\vec{p}+\vec{q})+β(\vec{p}-2\vec{q})+γ(\vec{p}\times\vec{q})\),
then the value of γ is ________.- JEE Advanced - 2024
- Mathematics
- 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
- Given \(|\vec b=2, |\vec b\times \vec a|=2,\) then the value of \(|\vec b\times \vec a-\vec b|^2\) is
- JEE Main - 2024
- Mathematics
- Vector Algebra
Let $\vec{u}=\hat{i}-\hat{j}-2 \hat{k}, \vec{v}=2 \hat{i}+\hat{j}-\hat{k}, \vec{v} \cdot \vec{w}=2$ and $\vec{v} \times \vec{w}=\vec{u}+\lambda \vec{v}$. Then $\vec{u} \cdot \vec{w}$ is equal to
- JEE Main - 2023
- Mathematics
- Vector Algebra
- Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors Then which one of the following statements is TRUE ?
- JEE Main - 2023
- Mathematics
- Vector Algebra
Questions Asked in JEE Main exam
- Find the acceleration of \(2\) \(kg\) block shown in the diagram (neglect friction)
- JEE Main - 2024
- Acceleration
- If \(|2A|^3 =21\) and \(\begin{bmatrix} 1 & 0 & 0 \\[0.3em] 0 & α & β \\[0.3em] 0 & β & α \end{bmatrix}\), then a is (if \(α,β∈I\))
- JEE Main - 2024
- Matrices
- Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:
- JEE Main - 2024
- Geometric Progression
- Two lines \(L_1 \;\& \;L_2\) passing through origin trisecting the line segment intercepted by the line \(4x + 5y = 20\) between the coordinate axes. Then the tangent of angle between the lines \(L_1\) and \(L_2\) is
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- Tangents and Normals
- Rank of the word 'GTWENTY' in dictionary is _____ .
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- permutations and combinations
Concepts Used:
Vector Algebra
A vector is an object which has both magnitudes and direction. It is usually represented by an arrow which shows the direction(→) and its length shows the magnitude. The arrow which indicates the vector has an arrowhead and its opposite end is the tail. It is denoted as
The magnitude of the vector is represented as |V|. Two vectors are said to be equal if they have equal magnitudes and equal direction.
Vector Algebra Operations:
Arithmetic operations such as addition, subtraction, multiplication on vectors. However, in the case of multiplication, vectors have two terminologies, such as dot product and cross product.
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