Download App

Vector — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsVector1 Mark
Question
Assertion : If $\vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C}$, then $\vec{A}$ may not always be equal to $\vec{C}$
Reason : The dot product of two vectors involves cosine of the angle between the two vectors.
✓

Answer

$ \vec{A} \cdot \vec{B}=\vec{B} \cdot \vec{C} \Rightarrow A B \cos \theta_1=B C \cos \theta_2 $
$ \therefore A=C, \text { only when } \theta_1=\theta_2$
So when angle between $\vec{A}$ and $\vec{B}$ is equal to angle between $\vec{B}$ and $\vec{C}$ only then $\vec{A}$ equal to $\vec{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Assertion & Reason" from Vector→Vector — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Assertion : A body may be accelerated even when it is moving uniformly.
Reason : When direction of motion of the body is changing then body may have acceleration.
→
Assertion : Red shift confirms that the universe is expanding
Reason : Wavelength of red light is maximum in the visible region
→
Assertion : Parallex method cannot be used for measuring distances of stars more than 100 light years away.
Reason : Because parallex angle reduces so much that it cannot be measured accurately.
→
Assertion : The velocity increases, when water flowing in broader pipe enter a narrow pipe.
Reason $\quad$ : According to equation of continuity, product of area and velocity is constant.
→
Assertion : Inertia is the property by virtue of which the body is unable to change by itself the state of rest only.
Reason : The bodies do not change their state unless acted upon by an unbalanced external force.
→
Assertion : A block of wood is floating in a tank containing water. The apparent weight of the floating block is equal to zero.
Reason : Because the entire weight of the block is supported by the buoyant force (the upward thrust) due to water.
→
Assertion $\quad:$ ac is more dangerous than $dc$
Reason : Frequency of ac is dangerous for human body.
→
Assertion : Power developed in circular motion is always zero.
Reason : Work done in case of circular motion is zero.
→
Assertion : Lenz's law violates the principle of conservation of energy.
Reason : Induced e.m.f., opposes always the change in magnetic flux responsible for its production.
→
Assertion : Pascal law is the working principle of a hydraulic lift.
Reason : Pressure is equal to thrust per area.
→