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JEE PHYSICS MCQ: MOTION IN PLANE

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Two vectors are given by A⃗=(3i^+j^+3k^)\vec{A}=(3 \hat{i}+\hat{j}+3 \hat{k}) and B⃗=(3i^+5j^−2k^)\vec{B}=(3 \hat{ i }+5 \hat{ j }-2 \hat{ k }). Find the third vector C⃗\vec{ C } if A⃗+3B⃗−C⃗=0\vec{ A }+3 \vec{ B }-\vec{ C }=0
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Correct option: C
(12i^+16j^−3k^)(12 \hat{i}+16 \hat{j}-3 \hat{k})
Option C ((12i^+16j^−3k^)(12 \hat{i}+16 \hat{j}-3 \hat{k})) is correct because it is the result of the vector addition and scalar multiplication as described in the equation C⃗=A⃗+3B⃗\vec{C} = \vec{A} + 3\vec{B}.

More Questions from MOTION IN PLANE

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Given, P⃗=A⃗+B⃗  and P=A+B.\mathrm{\vec P} = \mathrm{\vec A} + \mathrm{\vec B}\,\,\mathrm{and}\,P = A + B. The angle between A⃗ and B⃗\mathrm{\vec A}\,and\,\mathrm{\vec B} is Assertion: The necessary condition for motion in two dimensions, velocity and acceleration vectors should have any angle between 0∘0^{\circ} and 90∘90^{\circ} between them.
Reason: For two-dimensional or three-dimensional motion, velocity and acceleration of an object works in opposite direction.
If (a+3b)⋅(7a−5b)=0\mathrm{If}\,(\mathbf{a}+3 \mathbf{b}) \cdot(7 \mathbf{a}-5 \mathbf{b})=0 and
(a−4b)⋅(7a−2b)=0(\mathbf{a}-4 \mathbf{b}) \cdot(7 \mathbf{a}-2 \mathbf{b})=0. Then, the angle between a\mathbf{a} and b\mathbf{b} is
At the top of the trajectory of a projectile, the direction of its velocity and acceleration are A ball is thrown at an angle θ\theta and another ball is thrown at an angle (90∘−θ)\left(90^{\circ}-\theta\right) with the horizontal direction from the same point with velocity 39.2 ms−139.2 \mathrm{~ms}^{-1}. The second ball reaches 50 m50 \mathrm{~m} higher than the first ball. Find their individual heights. Take g=9.8 ms−2{g}=9.8 \mathrm{~ms}^{-2}. Assertion: The drover in a vehicle moving with a constant speed on a straight road is in a non-inertial frame of reference.

Reason: A reference frame in which Newton's laws of motion are applicable is non-inertial.
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