NDA 2016 Paper 1 | Vector Algebra Question 16 | Mathematics

What is a vector of unit length orthogonal to both the vectors $$\widehat i + \widehat j + \widehat k$$ and $$2\widehat i + 3\widehat j - \widehat k$$ ?

$${{ - 4\widehat i + 3\widehat j - \widehat k} \over {\sqrt {26} }}$$

$${{ - 4\widehat i + 3\widehat j + \widehat k} \over {\sqrt {26} }}$$

$${{ - 3\widehat i + 2\widehat j - \widehat k} \over {\sqrt {14} }}$$

$${{ - 3\widehat i + 2\widehat j + \widehat k} \over {\sqrt {14} }}$$

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

If a, b and c are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

a + b + c = 0

a + b + c = unit vector

a + b = c

a = b + c

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the area of the parallelogram having diagonals $$3\widehat i + \widehat j - 2\widehat k$$ and $$\widehat i - 3\widehat j + 4\widehat k$$ ?

5$$\sqrt 5 $$ sq. units

4$$\sqrt 5 $$ sq. units

5$$\sqrt 3 $$ sq. units

15$$\sqrt 2 $$ sq. units

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Let $$\widehat a$$ and $$\widehat b$$ of two unit vectors and $$\theta$$ be the angle between them.

What is $$\cos \left( {{\theta \over 2}} \right)$$ equal to ?

$${{\left| {\widehat a - \widehat b} \right|} \over 2}$$

$${{\left| {\widehat a + \widehat b} \right|} \over 2}$$

$${{\left| {\widehat a - \widehat b} \right|} \over 4}$$

$${{\left| {\widehat a + \widehat b} \right|} \over 4}$$

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