Vectors Quiz 1

Question 1

If the angle formed between the vectors $$\overrightarrow{a}=\left( 1,k \right)$$and $$\overrightarrow{b}=\left( 1,3 \right)$$ is $${{90}^{\circ }}$$.Then find the value of $$k$$?

Accepted Answer

$$-\dfrac{1}{3}$$

Answer

$$\dfrac{1}{3}$$

Answer

$$3$$

Answer

$$-3$$

Question 2

If the angle made by a vector with X axis is  $${{	ext{45}}^{\circ }}$$.Then find the vector?

Accepted Answer

$$i+j$$

Answer

$$3i+j$$

Answer

$$i+3j$$

Answer

$$9i+2j$$

Question 3

$$	ext{Find }\alpha +\beta 	ext{ if }\left( 4i+12j+9k ight)	imes \left( 5i+\alpha j+\beta k ight)=\overrightarrow{0}	ext{ ?}$$

Accepted Answer

$$\dfrac{105}{4}$$

Answer

$$\dfrac{60}{4}$$

Answer

$$\dfrac{95}{4}$$

Answer

$$\dfrac{45}{4}$$

Question 4

If the magnitude of vectors a, b and c are equal and satisfies the conditions $$a+b+\sqrt{2}c=0$$and $$a.b=1$$. Then find the angle between a and b?

Accepted Answer

$${{90}^{\circ }}$$

Answer

$${{60}^{\circ }}$$

Answer

$${{0}^{	ext{o}}}$$

Answer

$$	ext{None of these }$$

Question 5

If the magnitude of vectors a, b and c are equal and satisfies the conditions $$a+b+\sqrt{2}c=0$$and $$a.b=1$$. Then find the angle between a and b?

Accepted Answer

$$\dfrac{128}{5}\widehat{i}-\dfrac{64\sqrt{2}}{5}\widehat{j}+\dfrac{32}{5}\widehat{k}$$

Answer

$$\dfrac{128}{25}\widehat{i}-\dfrac{64\sqrt{2}}{25}\widehat{j}+\dfrac{32}{25}\widehat{k}$$

Answer

$$\dfrac{128}{5}\widehat{i}+\dfrac{64\sqrt{2}}{5}\widehat{j}+\dfrac{32}{5}\widehat{k}$$

Answer

$$\dfrac{128}{5}\widehat{i}-\dfrac{64\sqrt{2}}{5}\widehat{j}-\dfrac{32}{5}\widehat{k}$$