Quiz about Vector Algebra

Question 1

The scalar projection of the vector $$3 \hat{i}-\hat{j}-2 \hat{k}$$ on the vector $$\hat{i}+2 \hat{j}-3 \hat{k}$$ is

Accepted Answer

Covalent bond

Answer

$$\frac{7}{\sqrt{14}}$$

Answer

$$\frac{7}{14}$$

Answer

$$\frac{6}{13}$$

Answer

$$\frac{7}{2}$$

Question 2

If two vectors $$\vec{a}$$ and $$\vec{b}$$ are such that $$|\vec{a}|=2,|\vec{b}|=3$$ and $$\vec{a} \cdot \vec{b}=4$$, then $$|\vec{a}-2 \vec{b}|$$ is equal to

Accepted Answer

Covalent bond

Answer

$$2 \sqrt{6}$$

Answer

$$\sqrt{2}$$

Answer

$$24$$

Answer

$$2 \sqrt{2}$$

Question 3

If $$\vec{a}=\hat{i}-\hat{j}+7 \hat{k}$$ and $$\vec{b}=5 \hat{i}-\hat{j}+\lambda \hat{k}$$, then find the value of $$\lambda$$ so that the vectors $$\vec{a}+\vec{b}$$ and $$\vec{a}-\vec{b}$$ are orthogonal.

Accepted Answer

Covalent bond

Answer

$$\pm 5$$

Answer

$$\pm 6$$

Answer

$$\pm 7$$

Answer

$$\pm 8$$

Question 4

Find $$|\vec{x}|$$ if $$(\vec{x}-\vec{a}) \cdot(\vec{x}+\vec{a})=12$$, where $$\vec{a}$$ is a unit vector.

Accepted Answer

Covalent bond

Answer

$$\sqrt{13}$$

Answer

$$\sqrt{11}$$

Answer

$$\sqrt{10}$$

Answer

$$\sqrt{8}$$

Vector Algebra Cbse Class 12 Maths Problems and Solutions

Many students find Vector Algebra for Cbse Class 12 particularly challenging. Strengthen your concepts and gain confidence for your exams by solving free questions for Vector Algebra from for Cbse Class 12 preparation.