Question

can anyone answer the fourth question? It's of class 11 physics, ch- motion in a plane​

Answer 1

Given us two vectors,

• A = -2i + 3j - 4k
• B = 3i - 4j + 5k

We have to find the following,

[1] A + B

Here,

• A = -2i + 3j - 4k
• B = 3i - 4j + 5k

⇒ A + B = (-2 + 3)i + (3 - 4)j + (-4 + 5)k

⇒ A + B = i - j + k

For two vectors, A and B where

• A = Aₓi + Aᵧj + A₂k
• B = Bₓi + Bᵧj + B₂k

Addition of A and B can be calculated as,

⇒ A + B = (Aₓ + Bₓ)i + (Aᵧ + Bᵧ)j + (A₂ + B₂)k

[2] A - B

Here,

• A = -2i + 3j - 4k
• B = 3i - 4j + 5k

⇒ A - B = (-2 - 3)i + (3 - (-4))j + (-4 - 5)k

⇒ A - B = -5i + 7j - 9k

Similarly, For two vectors A and B where

• A = Aₓi + Aᵧj + A₂k
• B = Bₓi + Bᵧj + B₂k

Subtraction of vector is given as,

⇒ A - B = (Aₓ - Bₓ)i + (Aᵧ - Bᵧ)j + (A₂ - B₂)k

[3] A × B

Here,

• A = -2i + 3j - 4k
• B = 3i - 4j + 5k

| i j k |

⇒ A× B = | -2 3 -4 |

| 3 -4 5 |

⇒ A × B = (3×5 - (-4×-4))i - (-2×5 - 3×-4)j + (-2×-4 - 3×3)k

⇒ A × B = (15 - 16)i - (-10 + 12)j + (8 - 9)k

⇒ A × B = -i - 2j - k

[4] A . B

We have,

• A = -2i + 3j - 4k
• B = 3i - 4j + 5k

So,

⇒ A . B = (-2×3) + (3×-4) + (-4×5)

⇒ A . B = -6 - 12 - 20

⇒ A . B = -18 - 20

⇒ A . B = -38

For two vectors A and B, where

• A = Aₓi + Aᵧj + A₂k
• B = Bₓi + Bᵧj + B₂k

A . B can be calculated as,

⇒ A . B = AₓBₓ + AᵧBᵧ + A₂B₂

[5] 3A + 2B

Given,

• A = -2i + 3j - 4k
• B = 3i - 4j + 5k

So, Multiplying A by 3 and B by 2, we have

• 3A = -6i + 9j - 12k
• 2B = 6i - 8j + 10k

Now, 3A + 2B can be calculated in the same as we did in the [1]

⇒ 3A + 2B = (-6 + 6)i + (9 - 8)j + (-12 + 10)k

⇒ 3A + 2B = j - 2k