If vectors i^ + j^ + k^, i^ - j^ + k^ and 2i^ + 3j^ + λk^ are coplanar, then λ is equal to
- 2
3
2
- 3
Given, a→ ⊥ b→, a→ = 1 and if a→ + 3b→2a→ - b→ = - 10, b→ is equal to
1
4
a→ + b→ b→ + c→ c→ + a→ = a→ b→ c→, then
a→ b→ c→ = 1
a→ b→ c→ are coplanar
a→ b→ c→ = - 1
a→ b→ c→ are mutually perpendicular
Area of rhombus is ..., where diagonals are a→ = 2i^ - 3j^ + 5k^ and b→ = - i^ + j^ + k^
21.5
31.5
28.5
38.5
a→ . b→ × c→b→ . c→ × a→ + b→ . a→ × b→a→ . b→ ×c → is equal to
0
∞
If a→ = b→ = 1 and a→ + b→ = 3, then the value of 3a→ - 4b→ . 2a→ + 5b→ is
- 21
- 212
21
212
If a→ is perpendicular to b→ and c→, a→ = 2, b→ = 3, c→ = 4 and the angle between b→ and c→ is 2π3, then [a→ b→ c→] is equal to
43
63
123
183
If a→, b→ and c→ are perpendicular to b→ + c→, c→ + a→ and a→ + b→ respectively and if a→ + b→ = 6, b→ + c→ = 8 and c→ + a→ = 10 then a→ + b→ + c→ is equal to
52
50
102
10
D.
Given, a→ + b→ = 6⇒ a→2 + b→2 + 2a→ . b→ = 36 ...(i)Similarly, b→2 + c→2 + 2b→ . c→ = 64 ...(ii)and c→2 + a→2 + 2c→ . a→ = 100 ...(iii)On adding Eqs. (i), (ii) and (iii), we geta→2 + b→2 + c→2 + a→ . b→ + b→ . c→ + c→ . a→ = 100⇒ a→2 + b→2 + c→2 = 100 ...(iv) ∵ a→ . b→ + b→ . c→ + c→ . a→ = 0⇒ a→ + b→ + c→2 = a→2 + b→2 + c→2 + 2a→ . b→ + b→ . c→ + c→ . a→⇒ a→ + b→ + c→2 = 100 ∵ from Eq.(iv)⇒ a→ + b→ + c→ = 10
If the vectors a→ + λb→ + 3c→, - 2a→ + 3b→ - 4c→ and a→ - 3b→ + 5c→ are coplanar, then the value of λ is
- 1
If a→ + b→ + c→ = 0→, a→ = 3, b→ = 5, c→ = 7, then anle between a→ and b→ is
π6
2π3
5π3
π3
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