Two vectors $\overrightarrow A $and $\overrightarrow B $lie in a plane, another vector $\overrightarrow C $lies outside this plane, then the resultant of these three vectors i.e.,$\overrightarrow A + \overrightarrow B + \overrightarrow C $
- ACan be zero
- BCannot be zero
- CLies in the plane containing $\overrightarrow A + \overrightarrow B $
- DLies in the plane containing $\vec C$
Similar Questions
Explain subtraction of vectors.
Explain subtraction of vectors.
Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.
Column $-I$
Column $-II$
$(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $
$(i)$ Image
$(b)$ $\vec a \, - \,\,\vec c \, = \,\,\vec b$
$(ii)$ Image
$(c)$ $\vec b \, - \,\,\vec a \, = \,\,\vec c $
$(iii)$ Image
$(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$
$(iv)$ Image
Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.
| Column $-I$ | Column $-II$ |
| $(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $ | $(i)$ Image |
| $(b)$ $\vec a \, - \,\,\vec c \, = \,\,\vec b$ | $(ii)$ Image |
| $(c)$ $\vec b \, - \,\,\vec a \, = \,\,\vec c $ | $(iii)$ Image |
| $(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$ | $(iv)$ Image |
Given $a+b+c+d=0,$ which of the following statements eare correct:
$(a)\;a, b,$ c, and $d$ must each be a null vector,
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$
$(c)$ The magnitude of a can never be greater than the sum of the magnitudes of $b , c ,$ and $d$
$(d)$ $b + c$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear, and in the line of a and $d ,$ if they are collinear ?
Given $a+b+c+d=0,$ which of the following statements eare correct:
$(a)\;a, b,$ c, and $d$ must each be a null vector,
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$
$(c)$ The magnitude of a can never be greater than the sum of the magnitudes of $b , c ,$ and $d$
$(d)$ $b + c$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear, and in the line of a and $d ,$ if they are collinear ?
Six vectors, $\overrightarrow a$ through $\overrightarrow f$ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?
Six vectors, $\overrightarrow a$ through $\overrightarrow f$ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?
- [AIPMT 2010]
The angle between vector $\vec{Q}$ and the resultant of $(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})$ and $(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$ is:
The angle between vector $\vec{Q}$ and the resultant of $(2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})$ and $(2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})$ is:
- [JEE MAIN 2024]