NIMCET 2025 — Mathematics PYQ

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Question

NIMCET 2025 — Mathematics PYQ

NIMCET | Mathematics | 2025

If $\vec{a}, \vec{b}$ and $\vec{c}$ are three vectors such that $\vec{a} \times \vec{b} = \vec{c}$ , $\vec{a} \cdot \vec{c} = 2$ and $\vec{b} \cdot \vec{c} = 1$ . If $|\vec{b}| = 1$ , then find the value of $|\vec{a}|$ .

Choose the correct answer:

Explanation

Solution

Given:

$u n d e f in e d$
$u n d e f in e d$

From properties of the cross product:

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

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

However, the question provides:

\vec{a} \cdot \vec{c} = 2

\vec{b} \cdot \vec{c} = 1

Mathematical Contradiction:

Since $u n d e f in e d$ is the result of $u n d e f in e d$ , the dot product with its components must be zero:

\vec{a} \cdot (\vec{a} \times \vec{b}) = 0 \neq 2

\vec{b} \cdot (\vec{a} \times \vec{b}) = 0 \neq 1

If we ignore the orthogonality rule and force a calculation using $u n d e f in e d$ :

|\vec{a}| |\vec{b}| \sin \theta = |\vec{c}|

Assuming $u n d e f in e d$ ( $u n d e f in e d$ ):

|\vec{a}| (1) (1) = |\vec{c}| \implies |\vec{a}| = |\vec{c}|

If the question meant $u n d e f in e d$ :

|\vec{a}| = 2

Final Answer (Based on Option A):

|\vec{a}| = 2

Choose the correct answer:

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