JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Hard

1 of 1

Application +4 | -1

Let the unit vectors

\vec{a}, \vec{b}, \vec{c}

be the position vectors of the vertices of a triangle

A B C

. If

\vec{F}

is the position vector of the mid point of the line segment joining its orthocentre and centroid then

(\vec{a}-\vec{F})^2+(\vec{b}-\vec{F})^2+(

\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{F}})^2=

View answer and explanation

Correct option: C

Option C (3) is correct. By setting the circumcenter as the origin and using the properties of the orthocenter and centroid, we can simplify the expression and find its value.

More Questions from ADDITION OF VECTORS

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Let

\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}

and

\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}

. If

\mathbf{d}

a

unit vector such that

\mathbf{a} \cdot \mathbf{d}=0=(b \mathbf{c}

) , then

\mathbf{d}

is equal to
A vector

{\mathbf{\vec a}}

has components

2\;p

and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense, if this respect to new system

{\mathbf{\vec a}}

has components

p + 1

and 1, then If

\vec{a}, \vec{b}

and

\vec{c}

are three mutually perpendicular unit vetors and

\vec{d}

is a unit vector which makes equal angles with

\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}

ānd

\overrightarrow{\mathrm{c}}

then the value of

|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|^2

The non-zero vectors are

\vec{a}, \vec{b}

and

\vec{c}

are related by

\vec{a}=8 \vec{b}

and

\vec{c}=-7 \vec{b}

. Then the angle between

\vec{a}

and

\vec{c}

is If the vectors

2 \mathbf{i}+\mathbf{j}-\mathbf{k},-\mathbf{i}+2 \mathbf{j}+\lambda \mathbf{k}

and

-5 \mathbf{i}+2 \mathbf{j}-\mathbf{k}

ar coplanar, then the value of

\lambda

is equal The medium

AD

of the triangle

ABC

is bisected at

E,\;BE

meets

AC

F

, then

AF:AC =