Question

find a vector in direction of vector 4i-j+3k which has magnitude 7 units​

Answer 1

The vector in direction of vector 4i-j+3k which has magnitude 7 units​ will be (28/√26)i - (7/√26)j + (21/√26)k.

Given vector =  4i - j + 3k

So, the magnitude of this vector is √(4² + -1² + 3²) = √26

So, unit vector in direction to the above vector will be =

(1/magnitude of the vector) × (vector)

= 1/√26 [ 4i - j + 3k ]

= 4i/√26 - j/√26 + 3k/√26

This is the unit vector, it has magnitude of 1.

So, the vector with magnitude 7 will be 7 × Unit vector

= 7 × [4i/√26 - j/√26 + 3k/√26]

= (28/√26)i - (7/√26)j + (21/√26)k

This is the required vector.