1
NDA 2017 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
If $$a = 2\widehat i + 3\widehat j + 4\widehat k$$ and $$b = 3\widehat i + 2\widehat j - \lambda \widehat k$$ are perpendicular, then what is the value of $$\lambda$$ ?
A
2
B
3
C
4
D
5
2
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let | a | $$\ne$$ 0, | b | $$\ne$$ 0. (a + b) . (a + b) = | a |2 + | b |2 holds if and only if
A
a and b are perpendicular
B
a and b are parallel
C
a and b are inclined at an angle of 45$$^\circ$$
D
a and b are anti-parallel
3
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$r = x\widehat i + y\widehat j + z\widehat k$$, then what is $$r\,.\,\left( {\widehat i + \widehat j + \widehat k} \right)$$ equal to ?
A
x
B
x + y
C
$$-$$ (x + y + z)
D
(x + y + z)
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
A unit vector perpendicular to each of the vectors $$2\widehat i - \widehat j + \widehat k$$ and $$3\widehat i - 4\widehat j - \widehat k$$ is
A
$${1 \over {\sqrt 3 }}\widehat i + {1 \over {\sqrt 3 }}\widehat j - {1 \over {\sqrt 3 }}\widehat k$$
B
$${1 \over {\sqrt 2 }}\widehat i + {1 \over 2}\widehat j + {1 \over 2}\widehat k$$
C
$${1 \over {\sqrt 3 }}\widehat i - {1 \over {\sqrt 3 }}\widehat j - {1 \over {\sqrt 3 }}\widehat k$$
D
$${1 \over {\sqrt 3 }}\widehat i + {1 \over {\sqrt 3 }}\widehat j + {1 \over {\sqrt 3 }}\widehat k$$
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