Question

Question:-
Don't post irrelevant answers
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Answer 1

[1]

We have three vectors A , B and C that have equal magnitude.

Also, It is given that,

⇒ A + B = C

Assume that the magnitude of these three vectors are x and the angle between them is θ.

According to the question, We have to find θ.

So, We know, Addition of A and B is given by

⇒ A + B = C

⇒ √(|A|² + |B|² + 2|A| |B| cos θ) = |C|

Squaring both sides,

⇒ (x)² + (x)² + 2 • x • x • cos θ = x²

We assumed,

• |A| = |B| = |C| = x

⇒ 2x² + 2x² cos θ = x²

⇒ 2x² ( 1 + cos θ ) = x²

⇒ 1 + cos θ = 1 / 2

⇒ cos θ = - 1 / 2

⇒ θ = 120°

Hence, Option (D) is correct.

[2]

We are given two vectors of magnitude 6 and 8 respectively. The magnitude of the resultant vector is 10.

Same as the question (1), you can also solve it using that formula but I will tell you the shorter trick.

If you carefully observe,

⇒ Resultant² = (Vector A)² + (Vector B)²

⇒ 10² = 8² + 6²

⇒ 100 = 64 + 36

⇒ 100 = 100

Same as using the Pythagoras theorem in the triangle which is formed by these three vectors.

This is only possible when the vectors are at an angle of 90°.

Hence, Option (D) is correct.

[3]

Given,

• Vector A = 4 units
• Vector B = 5 units
• Angle b/w A & B, θ = 180°

Using the formula of vector additon, we have

⇒ A + B

⇒ √(|A|² + |B|² + 2|A| |B| cos θ)

⇒ √(4² + 5² + 2×4×5×cos 180°)

⇒ √(16 + 25 + 40×-1)

⇒ √(41 - 40)

⇒ √1 or 1 unit

∴ Option (A) is correct.

[4]

Given us two vectors A and B of magnitudes 2 and 3 respectively. The resultant of A and B had a magnitude of 5 units.

Here, the magnitudes of A and B are directly added. Which is possible only when the vectors are parallel and have 0° angle between them.

∴ Option (A) is correct.