(C) Given vectors are $\vec{a}=2 \hat{i}-2 \hat{j}+5 \hat{k}$ and $\vec{b}=-2 \hat{i}+5 \hat{j}-3 \hat{k}$.Sum of the vectors is $\vec{s} = \vec{a} +

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(C) Given vectors are $\vec{a}=2 \hat{i}-2 \hat{j}+5 \hat{k}$ and $\vec{b}=-2 \hat{i}+5 \hat{j}-3 \hat{k}$.Sum of the vectors is $\vec{s} = \vec{a} + \vec{b} = (2-2) \hat{i} + (-2+5) \hat{j} + (5-3) \hat{k} = 0 \hat{i} + 3 \hat{j} + 2 \hat{k} = 3 \hat{j} + 2 \hat{k}$.Since the $\hat{i}$ component of the resulting vector $\vec{s}$ is $0$,the vector lies in the $YZ$-plane.$A$ vector that lies in a plane is parallel to that plane.Therefore,the vector is parallel to the $YZ$-plane.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

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The vector in the direction of the sum of the vectors $\vec{a}=2 \hat{i}-2 \hat{j}+5 \hat{k}$ and $\vec{b}=-2 \hat{i}+5 \hat{j}-3 \hat{k}$ is

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A
Perpendicular to $ZX$-plane
B
Parallel to $ZX$-plane
C
Parallel to $YZ$-plane
D
Perpendicular to $YZ$-plane

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Using vectors,find the value of $k$ such that the points $(k,-10,3), (1,-1,3)$ and $(3,5,3)$ are collinear.

Difficult

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If $P$ and $Q$ are two points on the curve $y = 2^{x+2}$ in the rectangular Cartesian coordinate system such that $\overline{OP} \cdot \hat{i} = -1$ and $\overline{OQ} \cdot \hat{i} = 2$,then $\overline{OQ} - 4\overline{OP} = $

DifficultAP EAMCET 2022

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If $D, E, F$ are the midpoints of the sides $BC, CA, AB$ of a triangle $ABC$ respectively,find the position vector of the centroid of $\Delta DEF$,given that the position vectors of $A, B, C$ are $i + j, j + k, k + i$ respectively.

Medium

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Let $p = (x + 4y)\vec{a} + (2x + y + 1)\vec{b}$ and $q = (y - 2x + 2)\vec{a} + (2x - 3y - 1)\vec{b}$,where $\vec{a}$ and $\vec{b}$ are non-collinear vectors. If $3p = 2q$,then the values of $x$ and $y$ are:

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If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors and $|\overrightarrow{a}+\overrightarrow{b}|=1$,then $|\overrightarrow{a}-\overrightarrow{b}|$ is equal to

MediumKCET 2008

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The vector in the direction of the sum of the vectors $\vec{a}=2 \hat{i}-2 \hat{j}+5 \hat{k}$ and $\vec{b}=-2 \hat{i}+5 \hat{j}-3 \hat{k}$ is

Similar Questions

Using vectors,find the value of $k$ such that the points $(k,-10,3), (1,-1,3)$ and $(3,5,3)$ are collinear.

If $P$ and $Q$ are two points on the curve $y = 2^{x+2}$ in the rectangular Cartesian coordinate system such that $\overline{OP} \cdot \hat{i} = -1$ and $\overline{OQ} \cdot \hat{i} = 2$,then $\overline{OQ} - 4\overline{OP} = $

If $D, E, F$ are the midpoints of the sides $BC, CA, AB$ of a triangle $ABC$ respectively,find the position vector of the centroid of $\Delta DEF$,given that the position vectors of $A, B, C$ are $i + j, j + k, k + i$ respectively.

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