Motion in a Plane Test

Result

Motion in a Plane Test - 6

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Weekly Quiz Competition

Question 1
4 / -1

If are two vectors, then the value of × is

A

B

C

D

Solution
Question 2
4 / -1

If then select the correct alternative.

A
is parallel to

B
is perpendicular to

C
Component of Component of

D
Component of - Component of

Solution

According to definition of cross product is perpendicular to both
Question 3
4 / -1

If are two vectors, then which of the following is a correct statement?

A

B

C

D

Solution

Vector product of two vectors is anti- commutative.
i.e;
Question 4
4 / -1

If unit vectors are inclined at an angle θ,Then is

A
2sin θ/2

B
2cos θ/2

C
2tan θ/2

D
tan θ

Solution
Question 5
4 / -1

If the angle between the vectors is θ, the value of the product is equal to

A
BA² cos θ

B
BA² sin θ

C
BA² sin θ cos θ

D
zero

Solution

We know that scalar triple product is cyclic
Question 6
4 / -1

Find the projection of the vector on the vector is

A
19/9

B
38/9

C
8/9

D
4/9

Solution
Question 7
4 / -1

The area of the triangle formed by the adjacent sides with and B =is

A
√165/2 units

B
√137/2 units

C
√165 units

D
√137 units

Solution
Question 8
4 / -1

A body moves 6 m north. 8 m east and 10 m vertically upwards, what is its resultant displacement from initial position is

A
10√2 m

B
10 m

C
10/√2 m

D
20 m

Solution

The situation is as shown in the figure
Question 9
4 / -1

A man wants to reach from A to the opposite corner of the square C (Figure). The sides of the square are 100m each. A central square of 50m × 50m is filled with sand.

Outside this square, he can walk at a speed 1ms⁻¹. In the central square, he can walk only at a speed of v ms⁻¹(v < 1). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?

A
0.18 m s^-1

B
0.81 ms⁻¹

C
0.5 m s^-1

D
0.95 m s^-1

Solution

Consider the straight-line path APQC through the sand. Time is taken to go from A to C via this path

The shortest path outside the sand will be ARC. Time is taken to go from A to C via this path
Question 10
4 / -1

A
zero

B
A²B²

C
AB

D
√AB

Solution

Let θ be angle between vectors