1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If the vectors $$\alpha \widehat i + \alpha \widehat j + \gamma \widehat k$$, $$\widehat j + \widehat k$$ and $$\gamma \widehat i + \gamma \widehat j + \beta \widehat k$$ lie on a plane, where $$\alpha$$, $$\beta$$ and $$\gamma$$ are distinct non-negative numbers, then $$\gamma$$ is
A
arithmetic mean of $$\alpha$$ and $$\beta$$
B
geometric mean of $$\alpha$$ and $$\beta$$
C
harmonic mean of $$\alpha$$ and $$\beta$$
D
None of the above
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The vectors a, b, c and d are such that a $$\times$$ b = c $$\times$$ d and a $$\times$$ c = b $$\times$$ d. Which of the following is/are correct?

1. (a $$-$$ d) $$\times$$ (b $$-$$ c) = 0

2. (a $$\times$$ b) $$\times$$ (c $$\times$$ d) = 0

Select the correct answer using the code given below.
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
3
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$a = \widehat i + \widehat j$$, $$b = 3\widehat i + 4\widehat k$$ and $$b = c + d$$, where c is parallel to a and d is perpendicular to a.
What is c equal to ?
A
$${{3(\widehat i + \widehat j)} \over 2}$$
B
$${{2(\widehat i + \widehat j)} \over 3}$$
C
$${{(\widehat i + \widehat j)} \over 2}$$
D
$${{(\widehat i + \widehat j)} \over 3}$$
4
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$a = \widehat i + \widehat j$$, $$b = 3\widehat i + 4\widehat k$$ and $$b = c + d$$, where c is parallel to a and d is perpendicular to a.
If $$d = x\widehat i + y\widehat j + z\widehat k$$, then which of the following equations is/are correct?

I. $$y - x = 4$$

II. $$2z - 3 = 0$$

Select the correct answer using the code given below.
A
Only I
B
Only II
C
Both I and II
D
Neither I nor II
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