1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?
A
<2/3, 2/3, 1/3>
B
<1/3, 2/3, 2/3>
C
$\left\langle\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right\rangle$
D
$\left\langle\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}\right\rangle$
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following statements :

1. The direction ratios of y-axis can be <0, 4, 0>

2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0>

Which of the statements given above is/are correct?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
3
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
$\frac{\vec{\text{a}}−\vec{\text{b}}}{2}$
4
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
$\frac{\pi}{2}$
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