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JEE • MATHEMATICS • ADDITION OF VECTORS

Addition of vectors practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 3

Analyzing +4 | -1

If the points

P

and

Q

are respectively the circumcenter and the orthocentre of a

\triangle A B C

, then

\overrightarrow{P A}+\overrightarrow{P B}+\overrightarrow{P C}

is equal to

View answer and explanation

Correct option: C

\overrightarrow{P Q}

Option C (

\overrightarrow{{PQ}}

) is correct because the vector sum

\overrightarrow{{PA}} + \overrightarrow{{PB}} + \overrightarrow{{PC}}

is equal to

\overrightarrow{{PQ}}

based on the properties of the circumcenter, orthocenter, and centroid of a triangle.

2 Hard

2 of 3

Analyzing +4 | -1

\left|x_1\right|>\left|y_1\right|+\left|z_1\right|,\left|y_2\right|>\left|x_2\right|+\left|z_2\right|,\left|z_3\right|>\left|x_3\right|+\left|y_3\right|

,
then

x_1 \hat{\mathbf{i}}+y_1 \hat{\mathbf{j}}+z_1 \hat{\mathbf{k}}, x_2 \hat{\mathbf{i}}+y_2 \hat{\mathbf{j}}+z_2 \hat{\mathbf{k}}

and

x_3 \hat{\mathbf{i}}+y_3 \hat{\mathbf{j}}+z_3 \hat{\mathbf{k}}

are

View answer and explanation

Correct option: D

non-coplanar

The vectors are non-coplanar because the given inequalities contradict the condition for coplanarity, which requires the determinant to be zero.

3 Hard

3 of 3

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.

Revision notes and key takeaways

Review ADDITION OF VECTORS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 3 single-correct-answer MCQs on ADDITION OF VECTORS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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