1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
PQRS is a parallelogram. If $\overrightarrow{\text{PR}}=\vec{\text{a}}$ and $\overrightarrow{\text{QS}}=\vec{\text{b}}$, then what is $\overrightarrow{\text{PQ}}$ equal to ?
A
$\vec{\text{a}}+\vec{\text{b}}$
B
$\vec{\text{a}}−\vec{\text{b}}$
C
$\frac{\vec{\text{a}}+\vec{\text{b}}}{2}$
D
$\frac{\vec{\text{a}}−\vec{\text{b}}}{2}$
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let $\vec{\text{a}}$ and $\vec{\text{b}}$ are two unit vectors such that $\vec{\text{a}}+2 \vec{\text{b}}$ and $5\vec{\text{a}}−4\vec{\text{b}}$ are perpendicular. What is the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ ?
A
$\frac{\pi}{6}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{2}$
3
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
Let $\vec{\text{a}}$$\vec{\text{b}}$ and $\vec{\text{c}}$ be unit vectors lying on the same plane. What is $\{(3\vec{\text{a}} + 2\vec{\text{b}}) × (5\vec{\text{a}} − 4\vec{\text{c}})\}⋅(\vec{\text{b}} + 2\vec{\text{c}})$ equal to ?
A
−8
B
−32
C
8
D
0
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
What are the values of x for which the angle between the vectors 2x2$\hat{\text{i}}$ + 3x$\hat{\text{j}}$ + $\hat{\text{k}}$ and $\hat{\text{i}}$ −2$\hat{\text{j}}$ + x2$\hat{\text{k}}$ is obtuse ?
A
0 < x < 2
B
x < 0
C
x > 2
D
0 ≤ x ≤ 2
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