Question

A and B are vectors. If A=5i+6j+k and B=i+j-2k, then find the angel made by the vector (A-2B) with the +z axis.

Answer 1

Answer:

Vector (A-2.B) = 5i+6j+k-2i-2j+4k = (3i+4j+5k)……………(1)

| A -2.B| = √{3^2+4^2+5^2} = 5√2 units.

Let any vector along z-axis is vector C = c.k………….(2).

|C|=√{c^2}= c units.

Angle between vector (A-2B) and vector C = cos^-1{(A-2B).(C)}/|A-2B|.|C|.

= cos^-1{(3i+4j+5k).(ck)}/5√2.c.

= cos^-1(5.c/5√2.c).

= cos^-1(1/√2).

= 45°. Answer.

Answer 2

ur ans is 45

hope it helps u.....❤