If $\vec{A}=\hat{i}+\hat{j}+3 \hat{k}$,$\vec{B}=-\hat{i}+\hat{j}+4 \hat{k}$ and $\vec{C}=2 \hat{i}-2 \hat{j}-8 \hat{k}$,then the angle between the vectors $\vec{P}=\vec{A}+\vec{B}+\vec{C}$ and $\vec{Q}=(\vec{A} \times \vec{B})$ is (in degree) (in $^{\circ}$)
- A$0$
- B$45$
- C$90$
- D$60$
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Similar Questions
If $\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$,then the scalar and vector products of $\overrightarrow{ F }$ and $\overrightarrow{ r }$ have the magnitudes respectively as
MediumNEET 2022
View SolutionGiven that $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$ and that $\overrightarrow{C}$ is $\perp$ to $\overrightarrow{A}$. Further,if $|\overrightarrow{A}| = |\overrightarrow{C}|$,then what is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?
Medium
View SolutionIf $\theta$ is the angle between two vectors $\vec{A}$ and $\vec{B}$,then match the following two columns.
Column $I$ Column $II$ $(A)$ $\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$ $(p)$ $\theta = 45^{\circ}$ or $135^{\circ}$ $(B)$ $\vec{A} \cdot \vec{B} = B^2$ $(q)$ $\theta = 0^{\circ}$ $(C)$ $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$ $(r)$ $\vec{A} = \vec{B}$ $(D)$ $|\vec{A} \times \vec{B}| = AB$ $(s)$ $\theta = 90^{\circ}$
| Column $I$ | Column $II$ |
| $(A)$ $\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$ | $(p)$ $\theta = 45^{\circ}$ or $135^{\circ}$ |
| $(B)$ $\vec{A} \cdot \vec{B} = B^2$ | $(q)$ $\theta = 0^{\circ}$ |
| $(C)$ $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$ | $(r)$ $\vec{A} = \vec{B}$ |
| $(D)$ $|\vec{A} \times \vec{B}| = AB$ | $(s)$ $\theta = 90^{\circ}$ |
Medium
View SolutionWhich of the following is not true? Given $\overrightarrow A = 3\hat i + 4\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,where $A$ and $B$ are the magnitudes of $\overrightarrow A$ and $\overrightarrow B$.
Easy
View SolutionThe resultant of two vectors $A$ and $B$ is perpendicular to the vector $A$ and its magnitude is equal to half the magnitude of vector $B$. The angle between $A$ and $B$ is ....... $^o$
Difficult
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