Question Video: Adding Two Vectors Then Finding the Cross Product of Their Sum by a Third Vector | Nagwa Question Video: Adding Two Vectors Then Finding the Cross Product of Their Sum by a Third Vector | Nagwa

# Question Video: Adding Two Vectors Then Finding the Cross Product of Their Sum by a Third Vector Mathematics • Third Year of Secondary School

## Join Nagwa Classes

Given that π = 7π’ + 2π£, π = βπ’ + 2π£, and π = 6π’ + 6π£, determine (π + π) Γ π.

02:49

### Video Transcript

Given that vector π is equal to seven π’ plus two π£, vector π is equal to negative π’ plus two π£, and vector π is equal to six π’ plus six π£, determine the cross product of π plus π and π.

In this question, weβre given three vectors in two dimensions in terms of their π’- and π£-components. Firstly, we need to find the sum of vector π and vector π. We then need to find the cross product of this vector and vector π. Letβs begin by finding the sum of vectors π and π. This is equal to six π’ plus six π£ plus seven π’ plus two π£. We can find the sum of the π’- and π£-components separately. Six π’ plus seven π’ is equal to 13π’ and six π£ plus two π£ is eight π£, giving us the vector 13π’ plus eight π£.

Next, we need to find the cross product of this vector and vector π. This is the cross product of 13π’ plus eight π£ and negative π’ plus two π£. We recall that for two vectors π and π in the coordinate plane with π’ and π£ as unit vectors such that π is equal to ππ’ plus ππ£ and π is equal to ππ’ plus βπ£, then the cross product of vectors π and π is the determinant of the two-by-two matrix π, π, π, β multiplied by the unit vector π€. This is equal to πβ minus ππ multiplied by the unit vector π€.

In this question, we need to find the determinant of the two-by-two matrix 13, eight, negative one, two. This is equal to 13 multiplied by two minus negative one multiplied by eight, giving us 26 plus eight. And multiplying by the unit vector π€, this is equal to 34π€. If π is equal to seven π’ plus two π£, π is equal to negative π’ plus two π£, and π is equal to six π’ plus six π£, then the cross product of π plus π and π is 34π€.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions