# Multiplication with Vectors

## Trending Questions

**Q.**

Starting from $\left(-1\right)\times 5$, write various products showing some pattern to show $\left(-1\right)\times \left(-1\right)=1$.

**Q.**

The vector sum of two forces is perpendicular to their vector differences. In that case, the force

Are equal to each other in magnitude

Are not equal to each other in magnitude

Cannot be predicted

Are equal to each other

**Q.**

If $A$ and $B$ are complementary angles, then

$\mathrm{sin}\left(A\right)=\mathrm{sin}\left(B\right)$

$\mathrm{cos}\left(A\right)=\mathrm{cos}\left(B\right)$

$\mathrm{tan}\left(A\right)=\mathrm{tan}\left(B\right)$

$\mathrm{sec}\left(A\right)=\mathrm{cosec}\left(B\right)$

**Q.**

The area of the parallelogram is represented by the vectors $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+4\hat{j}$

$14\text{units}$

$7.5\mathrm{units}$

$10\mathrm{units}$

$5\mathrm{units}$

**Q.**Two forces −→F1=(2^i+2^j) N and −→F2=(3^j+4^k) N are acting on a particle. The component of force −→F1 along force −→F2 is

- 56
- 53
- 65
- 52

**Q.**

What jobs use radical expressions?

**Q.**Two tall buildings are 40 m apart. With what is speed must a ball be thrown horizontally from a window 145 m

above the ground in one building, so that it will enter a window 22.5 m from the ground in the other?

**Q.**The angles which the vector A = 3i+ 6j + 2k makes with the co-ordinate axes are

**Q.**If |→A|=4, |→B|=3 and the angle between →A and →B is 30∘, then the scalar product of these two vectors is

- 4
- 6
- 6√3
- 4√3

**Q.**A force of magnitude 12 N acts on a particle in the direction of a vector →A=2^i−4^j+4^k, which results in the change of position of the particle from (3, 3, 5) m to (2, −1, 4) m. The work done by the force is (in Joule )

- 25
- 40
- 20
- 30

**Q.**

What does scalar projection mean?

**Q.**A ball is thrown at angle above horizontal of some height with the some velocity. Time taken for ball to reach first wall and second wall is equal to T1 and T2respectively. Find T1+T2(T=time of flight)

- T
- 2T
- 3T
- 4T

**Q.**If →a and →b are two non-zero vectors, |→a×→b|2 is equal to which of the following?

- a2b2−(→a.→b)2
- a2b2+(→a.→b)2
- ab−(→a.→b)2
- a2b2−(→a.→b)

**Q.**23. Find dot product of A and B vectors if the magnitude of A vector is 2 and B is 5 and the cross product of A and B vectors is 8

**Q.**If →P.→Q=PQ, then the angle between →P and →Q is

- 0o
- 30o
- 45o
- 60o

**Q.**A body acted upon by a force of 50 N is displaced through a distance 10 m in a direction making an angle of 60∘ with the force. The work done by the force is

(Take W=→F.→S, where W is work done, →F is force and →S is the displacement)

- 200 J
- 100 J
- 300 J
- 250 J

**Q.**If →a, →b, →c be any three non - coplanar vectors, then calculate the value of [→a+→b →b+→c →c+→a] is

- 2[→a+→b+→c]
- 2[→a →b →c]
- 2√[→a+→b+→c]
- [→a+→b+→c]

**Q.**The component of a vector A along y-axis will have73maximum value if(1) A makes an angle of 30^° with y-axis(2) A makes an angle of 60^° with y-axis(3) A makes an angle of 0^° with y-axis8(4) A makes an angle of 90^° with y-axis4.A point which has velocities renr conto

**Q.**Let →a=^i+^j+^k, →b=^i−^j+^k and →c=^i−^j−^k be three vectors. A vector →v in the plane of →a and →b, whose projection on →c is 2√3, is given by

- ^i−3^j+3^k
- −3^i−3^j−^k
- 3^i−^j+3^k
- 4^i−2^j+4^k

**Q.**Angle between the vectors →a=−^i+2^j+^k and →b=x^i+^j+(x−2)^k

- is obtuse angle
- is acute angle
- is 90o
- depends upon x

**Q.**Two forces −→F1=(2^i+2^j) N and −→F2=(3^j+4^k) N are acting on a particle. The component of force −→F1 along force −→F2 is

- 56
- 53
- 65
- 52

**Q.**A parallelogram has diagonals expressed as →A=5^i−4^j+3^k and →B=3^i+2^j−^k. Area of parallelogram is

- √117 units
- √171 units
- √711 units
- √107 units

**Q.**Suppose $\overrightarrow{a}$ is a vector of magnitude 4.5 units due north. What is the vector (a) $3\overrightarrow{a}$, (b) $-4\overrightarrow{a}$?

**Q.**Projection of →A along the vector →B is

- →A⋅→B|→B|
- →A×→B|→B|
- →A⋅→B|→A|
- →A⋅→B→B

**Q.**two sides of a triangle represents two vectors 2i+3j+4k and 4i+3j+5k area of triangle is 1)9\sqrt2 ; 2)9\sqrt3 ; 3) 9/2 ; 4) 9\sqrt3/2

**Q.**If →P and →Q are two non-zero vectors, what is the angle between (→P+→Q) and (→P×→Q) ?

- 0
- π2
- π4
- π

**Q.**If →P and →Q are two non-zero vectors, what is the angle between (→P+→Q) and (→P×→Q) ?

- 0
- π2
- π4
- π

**Q.**A force (3^i+4^j) N acts on a body and displaces it by (3^i+4^j) meters. The work done by the force is

(Given that formula for work done is W=→F.→s)

- 5 J
- 25 J
- 10 J
- 30 J

**Q.**The direction of →A×→B for the vectors shown in the figure is

**Q.**A vector of magnitude 10 has its rectangular component as 8 and 6 along x and y axes. Find the angle that it makes with these axes.