Vector Algebra: 1 mark Questions (CBSE Class 12)

The value of p for which vectors $\hat{i}+2\hat{j}+3\hat{k}$ and $2\hat{i}-p\hat{j}+\hat{k}$ are perpendicular to each other is

1. (A)0
2. (B)1
3. (C)$\frac{5}{2}$
4. (D)$-\frac{5}{2}$

The value of m for which the points with position vectors $-\hat{i}-\hat{j}+2\hat{k}$, $2\hat{i}+m\hat{j}+5\hat{k}$ and $3\hat{i}+11\hat{j}+6\hat{k}$ are collinear, is

1. (A)8
2. (B)$-8$
3. (C)2
4. (D)$\frac{5}{2}$

If $|\vec{a}|=8,|\vec{b}|=3$ and $|\vec{a}\times \vec{b}|=12$, then the value of $|\vec{a}\cdot \vec{b}|$

1. (A)$6\sqrt{3}$
2. (B)$8\sqrt{3}$
3. (C)$12\sqrt{3}$
4. (D)$3\sqrt{12}$

If $|\vec{a}|=5$ and $-2\le \lambda \le 1$, then the sum of greatest and the smallest value of $|\lambda \vec{a}|$ is

1. (A)$-5$
2. (B)5
3. (C)10
4. (D)15

Vector of magnitude 3 making equal angles with $x$ and y axes and perpendicular to z axis is

1. (A)$\hat{i}+2\sqrt{2}\hat{j}$
2. (B)$3\hat{k}$
3. (C)$\frac{3\sqrt{2}}{2}\hat{i}+\frac{3\sqrt{2}}{2}\hat{j}$
4. (D)$\sqrt{3}\hat{i}+\sqrt{3}\hat{j}+\sqrt{3}\hat{k}$

For two vectors $\vec{a}$ and $\vec{b}$
Assertion (A) : $|\vec{a}\times \vec{b}{|}^2+(\vec{a}\cdot \vec{b}{)}^2=|\vec{a}{|}^2|\vec{b}{|}^2$
Reason (R) : $|\vec{a}\times \vec{b}|=(\vec{a}\cdot \vec{b})\tan \theta$, $\left(\theta \ne \frac{\pi }{2}\right)$

1. (A)Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true ?

1. (A)$\vec{a}\cdot \vec{b}\le |\vec{a}||\vec{b}|$
2. (B)$|\vec{a}+\vec{b}|\ge |\vec{a}|+|\vec{b}|$
3. (C)$|\vec{a}-\vec{b}|=|\vec{a}|-|\vec{b}|$
4. (D)$|\vec{a}\times \vec{b}|\ge |\vec{a}||\vec{b}|$

If $(\vec{a}+\vec{b})\cdot (\vec{a}-\vec{b})=198$ and $|\vec{a}|=10|\vec{b}|$, then :

1. (A)$|\vec{a}|=\sqrt{2}$
2. (B)$|\vec{b}|=\sqrt{2}$
3. (C)$|\vec{b}|=10\sqrt{2}$
4. (D)$|\vec{a}|=\frac{10}{\sqrt{2}}$

Assertion (A) : The vectors $\vec{a}$ and $(-2\vec{a})$, where $\vec{a}\ne \vec{0}$ are collinear vectors.
Reason (R) : $\vec{a}\cdot (-2\vec{a})=0$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

If $(3\hat{i}-2\hat{j}+5\hat{k})\times (4\hat{i}+p\hat{j}+q\hat{k})=\vec{0}$, then the values of p and q are :

1. (A)$p=-\frac{2}{3},q=\frac{5}{3}$
2. (B)$p=-\frac{8}{3},q=\frac{20}{3}$
3. (C)$p=\frac{20}{3},q=-\frac{8}{3}$
4. (D)$p=0,q=0$

Three points A(0, 1, 1), B(2, 0, $-1$) and C(1, 0, 3) form $△ABC$. The ar ($△ABC$) is :

1. (A)$\frac{\sqrt{53}}{2}$ sq. units
2. (B)$\sqrt{53}$ sq. units
3. (C)$\frac{\sqrt{11}}{2}$ sq. units
4. (D)$\sqrt{11}$ sq. units

If position vector $\vec{p}$ of a point (24, n) is such that $|\vec{p}|=25$, then the value of n is :

1. (A)$\pm 49$
2. (B)$\pm 5$
3. (C)$\pm 1$
4. (D)$\pm 7$

If vectors $\vec{a}=3\hat{i}+2\hat{j}+\lambda \hat{k}$ and $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$, represent the two strips of the Red Cross sign placed outside a doctor’s clinic, then the value of $\lambda$ is :

1. (A)1
2. (B)$\frac{5}{2}$
3. (C)$\frac{2}{5}$
4. (D)0