Vector Algebra Test

Result

Vector Algebra Test - 22

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Weekly Quiz Competition

Question 1
4 / -1

The area of the parallelogram whose adjacent side are

A
3

B
√2

C
4

D
√3

Solution
Question 2
4 / -1

A
a × b = b × c = c × a = 0

B
a × b = b × c = c × a ≠ 0

C
a × b = b × c = a × c = 0

D
a × b , b × c , c × a mutually perpendicular
Question 3
4 / -1

A
3

B
6

C
9

D
12
Question 4
4 / -1

|a| = |b| = 5 and the angle between a and b is π/4. The area of the triangle constructed on the vectors a – 2b and 3a + 2b is

A
50

B
50√2

C
50/√2

D
100

Solution
Question 5
4 / -1

In a triangle with vertices A (1, –1, 2), B(5, –6, 2) and C(1, 3, –1), find the altitude n = |BD|.

A
5

B
10

C
5√2

D
10/√2
Question 6
4 / -1

A
|a|²

B
2|a|²

C
3|a|²

D
4|a|²
Question 7
4 / -1

If a, b and c are three vectors such that a × b = c and b × c = a, then

A
a ≠ b ≠ c

B
a = b = c

C
a ≠ b ≠ c ≠ 1

D
a, b and c are orthogonal in pairs
Question 8
4 / -1

A
2/3

B
3/2

C
2

D
3
Question 9
4 / -1

If r∙a = r∙b = r∙c = 1. Where a , b and c are any three non - coplanar vectors, then r is

A
coplanar with a, b and c

B
parallel to a + b + c

C
parallel to b × c + c × a + a × b

D
parallel to (a × b) × c

Solution
Question 10
4 / -1

If a and b are vectors such that |a + b| = √29 and

A
0

B
3

C
4

D
8

Solution