Vectors (Basic)

Answer explanation

Answer explanation

Determine the value of t for which the vectors a = i + tj + 2k and b = 2i - 3j - 4k are perpendicular.

Answer explanation

If the 2 vectors are perpendicular to each other, their dot product will be zero.

Find the acute angle (to the nearest degree) between the vectors a = i - 2j + 3k and b = 2j - k.

Answer explanation

Since the question is asking for acute angle, we will need to take modulus of the dot product.

Find the length of projection of the vector a = i - 2j + 3k onto the vector b = 2j - k.

Answer explanation

The vector(s) perpendicular to both vectors a = i - k and b = 2i - j + k is

• -i - 3j - k

• i - j + 2k

• j + k

• i + 3j + k

Answer explanation

A parallelogram ABCD has the vertices at points A (1, 0, 1), B (0, 1, 0) and C (-1, 0, 1). Find the area of the parallelogram ABCD.

Answer explanation

Who is a left hander in this class?

• Kyan

• Ms Shirlyn

• Alice

Answer explanation

Ms Shirlyn is born left-handed but has been corrected to write with her right hand. She does everything else using her left hand but plays racquet games with both left and right hands. She is effectively ambidextrous! :)