Question

Show that the vector a 4i+3j-7k and b=4i-3j-k are perpendicular to each other.

Answer 1

To show: the vector a= 4i+3j-7k and b=4i-3j-k are perpendicular to each other.

Concept: For 2 vectors to be perpendicular their dot product should be zero.

Solution:

A = 4i + 3j - 7k

B = 4i - 3j - k

Dot product can be obtained as:

A.B = (4i + 3j - 7k).( 4i - 3j - k)

or, A.B = 16 - 9 - 7

or, A.B = 16 - 16

or, A.B = 0

Since, Dot product of given vectors is zero.

Therefore, They are perpendicular.

Answer 2

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⛦To show:

• the vector a= 4i+3j-7k and b=4i-3j-k are perpendicular to each other.

⛦Concept:

For 2 vectors to be perpendicular their dot product should be zero.

⛦Solution:

A = 4i + 3j - 7k

B = 4i - 3j - k

Dot product can be obtained as:

A.B = (4i + 3j - 7k).( 4i - 3j - k)

or, A.B = 16 - 9 - 7

or, A.B = 16 - 16

or, A.B = 0

Since, Dot product of given vectors is zero.

Therefore, They are perpendicular.