Which of the following statements is/are correct?

MATHEMATICS · Multi correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Which of the following statements is/are correct? (1) If

\mathbf{n}\cdot\mathbf{a}=0

\mathbf{n}\cdot\mathbf{b}=0

, and

\mathbf{n}\cdot\mathbf{c}=0

for some non-zero vector

\mathbf{n}

, then

[\mathbf{a}\ \mathbf{b}\ \mathbf{c}]=0

. (2) There exists a vector making angles

30^\circ

and

45^\circ

with the

x

-axis and

y

-axis, respectively. (3) The locus of a point for which

x=3

and

y=4

is a line parallel to the

Z

-axis whose distance from the

Z

-axis is

5

. (4) The vertices of a regular tetrahedron are

O

A

B

, and

C

, where

O

is the origin. The vector

\mathbf{OA}+\mathbf{OB}+\mathbf{OC}

is perpendicular to the plane

ABC