Question

Find the value of p so that the vectors A = 2i + pj + k and B = 4i - 2j -2k are perpendicular to
each other​

Answer 1

Explanation:

A = 2i + pj + k

B = 4i - 2j - 2k

if the vectors are perpendicular then A . B = 0

===> ( 2i + pj + k ) . ( 4i - 2j - 2k ) = 0

===> 8 - 2p - 2 = 0

===> 6 - 2p = 0

===> 2p = 6

===> p = 6/2 = 3

===> p = 3

* Some identity of Dot product of vector

==> i . i = 1

==> j . j = 1

==> k . k = 1

==> i . j = 0

==> i.k = 0

==> j . k = 0

Answer 2

Answer:

A = 2i + pj + k

B = 4i - 2j - 2k

if the vectors are perpendicular then A . B = 0

( 2i + pj + k ) . ( 4i - 2j - 2k ) = 0

8 - 2p - 2 = 0

6 - 2p = 0

2p = 6

p = 6/2 = 3

p = 3