Question

Find a vector of magnitude 5 units and parallel to the resultant of the vectors vector a is equal to two icap + 3 j cap - k cap and vector b is equal to icap - 2 j cap + k cap

Answer 1

Vector a = 2i+3j-k
Vector b = i-2j+k
Resultant = Vector a +Vector b
= (2i+3j-k)+(i-2j+k)
= 3i+j+0k
Magnitude of Resultant = √10
Unit vector in direction of resultant = 3i+j/√10
Vector of magnitude 5 in direction of resultant = 5(3i+j/√10)=(3√10i+√10j)/2

Answer 2

Dear Student,

◆ Answer -

X = √(5/2) (3i + j)

● Explanation -

# Given -

A = 2i + 3j - k

B = i - 2j + k

|X| = 5 units

# Solution -

Resultant of vector A and vector B is -

R = A + B

R = 2i + 3j - k + i - 2j + k

R = 3i + j

Unit vector in direction of R is -

r = (3i + j) / (√(3^2 + 1^2)

r = (3i + j) / √10

Then vector X is -

X = |X| r

X = 5 × (3i + j) / √10

X = √(5/2) (3i + j)

Thanks dear.