Test: Cross Product

QUESTION: 1

If | a | = 2, | b | = 5 and | a × b | = 8, thencan be equal to

A.
4
B.
7
C.
5
D.
± 6

Solution:

QUESTION: 2

If are unit vectors along X-axis, Y-axis and Z-axis respectively, then

Solution:

As we know that,

QUESTION: 3

The area of triangle whose adjacent sides are is :

A.
√70/2 sq. units
B.
9√2 /2 sq. units
C.
3√3 /2 sq. units
D.
2√3 /2 sq. units

Solution:

Area of triangle = ½(a * b)
a = (1, 0, -2) b = (2, 3, 1)
= i(0 + 6) + j(-4 - 1) + k(3 - 0)
= 6i - 5j + 3k
|a * b| = (36 + 25 + 9)^½
|a * b| = (70)^½
Area of triangle = ½(a * b)
= [(70)^½]/2

QUESTION: 4

The value of is:

A.
0
B.
3
C.
1/3
D.
1

Solution:

i.(j * k) + j.(k * i) + k(i * j)
= i.(i) + j.(j) + k.(k)
= 1 + 1 + 1
= 3

QUESTION: 5

The area of parallelogram whose sides areis:

A.
14 sq. units
B.
10√3 sq. units
C.
5√3 units
D.
7 sq. units

Solution:

A = {(1, -3, 4)} B = {(3, 1, -2)}
A * B = {(i^(6-4) - j^(-2 -12) + k^ (1+9)}
= 2i^ + 14j^ + 10k^
Area = [(2)² + (14)² + (10)²]^½
= (300)^½
= 10(3)^½ sq unit