If P(r) is a position vector of a point with scalar components (x,y,z), then the value of (r.i)(-i)-(r.j)j+(r.(-k))k, is: Option 1: x+y+z Option 2: -(x+y+z) Option 3: xi+yj+zk Option 4: -(xi+yj+zk)

Answer: -(xi+yj+zk). Solution: Here ri = x, rj = y and r*(-k) = -z. Substituting gives x(-i) - yj + (-z)k = -xi - yj - zk. This is -(xi+yj+zk).

Algebra

Vector Algebra

Easy

core

If $P(\vec{r})$ is a position vector of a point with scalar components $(x,y,z)$ , then the value of $(\vec{r}.\hat{i})(-\hat{i})-(\vec{r}.\hat{j})\hat{j}+(\vec{r}.(-\hat{k}))\hat{k}$ , is:

$x+y+z$

$-(x+y+z)$

$x\hat{i}+y\hat{j}+z\hat{k}$

$-(x\hat{i}+y\hat{j}+z\hat{k})$

✅ Correct Option: 4

Here $\vec{r}\cdot\hat{i} = x$ , $\vec{r}\cdot\hat{j} = y$ and $\vec{r}\cdot(-\hat{k}) = -z$ .

Substituting gives $x(-\hat{i}) - y\hat{j} + (-z)\hat{k} = -x\hat{i} - y\hat{j} - z\hat{k}$ .

This is $-(x\hat{i}+y\hat{j}+z\hat{k})$ .

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If $|\vec{a} - \vec{r}| = |\vec{a}| = |\vec{r}| = 1$ , then angle between $\vec{a}$ and $\vec{r}$ is

2026: 30 May Shift 1

Which of the following statements are correct?

A. The unit vector in the direction of the vector $\vec{a}=\hat{i}+\hat{j}+2\hat{k}$ is $\frac{1}{\sqrt{6}}\hat{i}+\frac{1}{\sqrt{6}}\hat{j}+\frac{2}{\sqrt{6}}\hat{k}$ .

B. A vector in the direction of the vector $5\hat{i}-\hat{j}+2\hat{k}$ which has magnitude 8 units is $40\hat{i}-8\hat{j}+16\hat{k}$ .

C. The vector joining the points P(2, 3, 0) and Q(–1, –2, –4) directed from P to Q is $-3\hat{i}-5\hat{j}-4\hat{k}$ .

D. The position vector of the mid-point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2) is $3\hat{i}+2\hat{j}-\hat{k}$ .

Choose the correct answer from the options given below:

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A vector of magnitude 8 units in the direction perpendicular to both the vectors $\hat{i} + \hat{j} + \hat{k}$ and $2\hat{i} + \hat{k}$ is

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If $\vec{a}$ is a unit vector perpendicular to both the vectors $\vec{b} = \hat{j} + \hat{2k}$ and $\vec{c} = \hat{i} + 2\hat{j}$ , then $\hat{a}$ is equal to

2022: 23 Aug Shift 1

If $\vec{a}$ is a unit vector and $(\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 8$ then $|\vec{x}|$ is

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) The value of $\hat{i}\cdot(\hat{j}\times\hat{k}) + \hat{j}\cdot(\hat{i}\times\hat{k}) + \hat{k}\cdot(\hat{i}\times\hat{j})$	(I) 16
(B) If $\lvert\vec{a}\rvert=10$ , $\lvert\vec{b}\rvert=2$ and $\vec{a}\cdot\vec{b}=12$ , then the value of $\lvert\vec{a}\times\vec{b}\rvert$ is	(II) $\frac{\pi}{4}$
(C) If $\theta$ is the angle between two vectors $\vec{a}$ and $\vec{b}$ , then the value of $\theta$ , for which $\vec{a}\cdot\vec{b} = \lvert\vec{a}\times\vec{b}\rvert$ is	(III) 14
(D) If $\vec{a}$ and $\vec{b}$ are perpendicular and $\vec{a} = 2\hat{i}+4\hat{j}+\lambda\hat{k}$ and $\vec{b} = 3\hat{i}-5\hat{j}+\hat{k}$ , then the value of $\lambda$ is	(IV) 1

Choose the correct answer from the options given below :

If P(r⃗)P(\vec{r})P(r) is a position vector of a point with scalar components (x,y,z)(x,y,z)(x,y,z), then the value of (r⃗.i^)(−i^)−(r⃗.j^)j^+(r⃗.(−k^))k^(\vec{r}.\hat{i})(-\hat{i})-(\vec{r}.\hat{j})\hat{j}+(\vec{r}.(-\hat{k}))\hat{k}(r.i^)(−i^)−(r.j^​)j^​+(r.(−k^))k^, is:

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CUET Mathematics Past Year Questions (Topic-Wise)

If $P(\vec{r})$ is a position vector of a point with scalar components $(x,y,z)$ , then the value of $(\vec{r}.\hat{i})(-\hat{i})-(\vec{r}.\hat{j})\hat{j}+(\vec{r}.(-\hat{k}))\hat{k}$ , is: