CUET PG 2023 — Mathematics PYQ

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CUET PG Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

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Question

CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

Each of the angle between vectors $a$ , $b$ and $c$ is equal to $6 0^{\circ}$ if $∣ a ∣ = 4$ , $∣ b ∣ = 2$ and $∣ c ∣ = 6$ then the modulus of $a + b + c$ is

Choose the correct answer:

Explanation

Step 1: Modulus ka Square nikalna

Sabse pehle hum $|\vec{a} + \vec{b} + \vec{c}|^2$ ka formula likhte hain:

|\vec{a} + \vec{b} + \vec{c}|^2 = |\vec{a}|^2 + |\vec{b}|^2 + |\vec{c}|^2 + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})

Step 2: Dot Products calculate karna

Humein pata hai ki $\cos(60^\circ) = \frac{1}{2}$ , toh individually dot products honge:

$\vec{a} \cdot \vec{b} = 4 \times 2 \times \frac{1}{2} = 4$
$\vec{b} \cdot \vec{c} = 2 \times 6 \times \frac{1}{2} = 6$
$\vec{c} \cdot \vec{a} = 6 \times 4 \times \frac{1}{2} = 12$

Step 3: Values ko formula mein rakhna

Ab saari values ko equation mein substitute karte hain:

|\vec{a} + \vec{b} + \vec{c}|^2 = 4^2 + 2^2 + 6^2 + 2(4 + 6 + 12)

|\vec{a} + \vec{b} + \vec{c}|^2 = 16 + 4 + 36 + 2(22)

|\vec{a} + \vec{b} + \vec{c}|^2 = 56 + 44

|\vec{a} + \vec{b} + \vec{c}|^2 = 100

Step 4: Final Result

Square root lene par:

|\vec{a} + \vec{b} + \vec{c}| = \sqrt{100} = 10

Choose the correct answer:

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