Vector Algebra Test

Result

Vector Algebra Test - 26

Score
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Weekly Quiz Competition

Question 1
4 / -1

If a = (1, p, 1), b = (q, 2, 2), a . b = r and a × b = (0, –3, 3), then p, q, and r are in that order

A
1, 5, 9

B
9, 5, 1

C
5, 1, 9

D
None of these
Question 2
4 / -1

A

B
0

C

D

Solution
Question 3
4 / -1

If [a × b b × c c × a] = λ[a b c]², then λ is equal to

A
0

B
1

C
2

D
3

Solution
Question 4
4 / -1

If r = αb × c + βc × a + γa × b and [a b c] = 2, then α + β + γ is equal to

A
r . [b × c + c × a + a × b]

B
1/2 r . (a + b + c)

C
2r . (a + b + c)

D
4
Question 5
4 / -1

The value of [(a – b) (b – c) (c – a)] is

A
0

B
1

C
2 [a b c]

D
2

Solution
Question 6
4 / -1

A
3

B
10

C
9

D
6
Question 7
4 / -1

If u, v and w are the three non - coplanar vectors, then (u + v – w) ∙ [(u – v) × (v – w)] is equal to

A
u ∙ w × u

B
u ∙ v × w

C
0

D
3 u ∙ v × w
Question 8
4 / -1

A
5

B
20

C
10

D
30
Question 9
4 / -1

A
A = 4, B = 2, C = 3, D = 1

B
A = 2, B = 3, C = 1, D = 4

C
A = 3, B = 4, C = 1, D = 2

D
A = 1, B = 4, C = 3, D = 2
Question 10
4 / -1

If a, b and c are three non - coplanar vectors and p, q and r are vectors defined by

A
0

B
1

C
2

D
3

Solution