NIMCET 2012 — Mathematics PYQ

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Question

NIMCET 2012 — Mathematics PYQ

NIMCET | Mathematics | 2012

If the vectors $\vec{a} = (1, x, -2)$ and $\vec{b} = (x, 3, -4)$ are mutually perpendicular, then the value of $x$ is:

Choose the correct answer:

Explanation

1. Concept:

Two non-zero vectors $\vec{a}$ and $\vec{b}$ are mutually perpendicular (orthogonal) if and only if their dot product is equal to zero.

\vec{a} \cdot \vec{b} = 0

2. Calculation:

Given the vectors:

$\vec{a} = (1, x, -2)$
$\vec{b} = (x, 3, -4)$

The dot product is calculated by summing the products of their corresponding components:

\vec{a} \cdot \vec{b} = (1)(x) + (x)(3) + (-2)(-4)

Set the dot product to zero for perpendicularity:

x + 3x + 8 = 0

3. Solve for $x$ :

Combine like terms:

4x + 8 = 0

4x = -8

x = \frac{-8}{4}

x = -2

Conclusion:

The value of $x$ is $-2$ .

Correct Option: (a)

Choose the correct answer:

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