MCQ
If a vector $2\hat i + 3\hat j + 8\hat k$ is perpendicular to the vector $4\hat j - 4\hat i + \alpha \hat k$. Then the value of $\alpha $ is
- A$-1$
- B$0.5$
- ✓$-0.5$
- D$1$
✓
Answer
Correct option: C.
$-0.5$
c
(c) Given vectors can be rewritten as $\overrightarrow A = 2\hat i + 3\hat j + 8\hat k$ and $\overrightarrow B = - 4\hat i + 4\hat j + \alpha \hat k$
(c) Given vectors can be rewritten as $\overrightarrow A = 2\hat i + 3\hat j + 8\hat k$ and $\overrightarrow B = - 4\hat i + 4\hat j + \alpha \hat k$
Dot product of these vectors should be equal to zero because they are perpendicular.
$\therefore \overrightarrow A \,.\,\overrightarrow B = - 8 + 12 + 8\alpha = 0$ $⇒$ $8\alpha = - 4$ $⇒$ $\alpha = - 1/2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The angular velocity of rotation of star (of mass $M$ and radius $R$) at which the matter start to escape from its equator will be
→The solid cylinder of length $80\, {cm}$ and mass ${M}$ has a radius of $20\, {cm}$. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $CD$ parallel to ${AB}$ as shown in figure is $2.7\, {kg} {m}^{2}$
→Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{ ms }\right)$ and choose the correct answer from the options given below:
→A body of mass $m$ is at rest. Another body of same mass moving with velocity $ V $ makes head on elastic collision with the first body. After collision the first body starts to move with velocity
→The state of an ideal gas was changed isobarically. The graph depicts three such isobaric lines. Which of the following is true about the pressures of the gas?
A projectile is given an initial velocity of $(\hat i + 2\hat j)\ ms^{-1}$, where $\hat i$ is along the ground and $\hat j$ is along the vertical. If $g = 10\ m/s^2$ , the equation of its trajectory is
→Three identical balls are projected with the same speed at angle $30^o, 45^o$ and $60^o$. Their ranges are $R_1 R_2$ and $R_3$ respectively. Then
→A block of mass $2 \,kg$ is kept on the floor. The coefficient of static friction is $0.4$. If a force F of $2.5$ Newtons is applied on the block as shown in the figure, the frictional force between the block and the floor will be ........ $N$
→When an elastic material with Young's modulus $Y$ is subjected to stretching stress $S,$ the elastic energy stored per unit volume of the material is:
→What is the $SI$ unit of permeability
→