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Vector Algebra question

2023 · 31 Jan · Shift 1 · Q35

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JEE Main
Mathematics
Vector Algebra
2023 · 31 Jan · Shift 1 · Q35

Vector Algebra question

2023 · 31 Jan · Shift 1 · Q35

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let

\vec{a}=2 \hat{i}+\hat{j}+\hat{k}

, and

\vec{b}

and

\vec{c}

be two nonzero vectors such that

|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|

and

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

. Consider the following two statements: (A)

|\vec{a}+\lambda \vec{c}| \geq|\vec{a}|

for all

\lambda \in \mathbb{R}

. (B)

\vec{a}

and

\vec{c}

are always parallel. Then,

A
only (B) is correct
B
both (A) and (B) are correct
C
only (A) is correct
D
neither (A) nor (B) is correct

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