# <span lang="EN-US

There are two vectors = 2 - 2 and = 7 + 2 - 3 and now we have to express as the sum of two vectors 1 and 2 such that 1 is parallel to and 2 is perpendicular to .

Let 1 = p + q + r and 2 = x + y + z

So, 1 = λ because both the vectors are parallel to each other and 2. = 0 because both the vectors are perpendicular to each.

This is the sum equation.

Taking dot product of on both sides, we get,

18 = 2p – q – 2r,

18 = 4λ + λ + 4λ,

λ = 2.

So, = 4 - 2 - 4

= 3 + 4

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Find the angle beMathematics - Board Papers

If two vectors <sMathematics - Board Papers

If <span lang="ENMathematics - Exemplar

Show that area ofMathematics - Exemplar

Find the equationMathematics - Board Papers

Using vectors, fiMathematics - Board Papers

Find the angle beMathematics - Board Papers

Find the positionMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers

If vectors <span Mathematics - Board Papers