Attempt following question by selecting a choice to answer.
D
Let
u,
v be two vectors. Which of the following is the value of
(3u + 6v) · (3u - 6v)?B DA.
D|3
u - 6
v|
2B.
D|3
u + 6
v|
2C.
D|3
u|
2 - |6
v|
2D.
D|3
u|
2 + |6
v|
2
D
C
Step 1: u, v are the two vectors.
Step 2: (3u + 6v) · (3u - 6v) = 3u · (3u - 6v) + 6v · (3u - 6v)[For any three vectors x, y, z, (x + y) · z = x · z + y · z.]
Step 3: = 3u · 3u - 3u · 6v + 6v · 3u - 6v · 6v
Step 4: = |3u|2 - 3u · 6v + 3u · 6v - |6v|2[For any vectors x, y, x · y = y · x.]
Step 5: = |3u|2 - |6v|2[For a vector x, x - x = 0.]